The unraveling of Carolingian hegemony in Europe occurred relatively quickly over the decade after Charles the Bald's death. This was due primarily to a series of deaths among prospective heirs, complicated by additional external and internal pressures.

Carolingian inheritance had the effect of fragmenting large territorial holdings. However, after Charlemagne's death Louis the Pious was the primary inheritor of Carolingian lands.

Louis, in turn, had four sons. Three were by his first wife (Lothaire, Louis the German, Pippin) and the fourth, Charles the Bald, was an offspring of a second marriage to Judith of Bavaria. Louis the Pious experienced revolt against his rule by his first sons when he sought to create an inheritance for Charles the Bald. The sons fought among themselves after Louis' death to settle the estate.

While the unraveling of Carolingian influence really starts with the deaths of Louis the Pious' sons, the decade 877 - 887 was particularly grim for the Carolingians. Here's a summary of Carolingian direct line male deaths over the years surrounding and including this decade. Below are the details.

Louis II of Italy, son of Lothaire I: 875
Louis the German, son of Lothaire I: 876
His son Carloman: 880
Another son, Louis the Younger: 882
Another son,  Louis the Fat: deposed 887, died 888
Charles the Bald: 877
His son abbot Carloman: 876
Another son, Louis the Stammerer: 879
Louis III: son of Louis the Stammerer: 882
Carloman, son of Louis the Stammerer: 884

I: Lothaire ruled as co-emperor with his father and received his choice of inheritances. He chose an swath of territory in the central part of the kingdom, running from the Low Countries in the north, through Burgundy, into Italy. He, in turn, had three sons. They were Lothaire II, Louis II and Charles of Provence. On his death in 855, his lands were divided among his three sons.

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Lothaire II (855-869)

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AR denier, 20mm, 1.24gr. Obv: HLOTHARIVS REX, central cross with four besants. Rev: VIRIDVN[VM] CIVIS, central temple. R1942; MG 1189; Dep 9B1, 1125 (11 examples); not in Bel. The latter two sources identify this as a scarce coin.  The mint is Verdun which after the Treaty of 843 went to Lothaire (a son of Louis the Pious). After 855 it passed to his son Lothaire II. After 869 it reverted to Charles the Bald. The coin is from Lotharingia, a territory including the Low Countries and northern Burgundy.

Lothaire II claimed the northern portion of his father's lands, which came to be known as Lotharingia. Lothaire II died in 869 without a legitimate heir. He had a bastard son Hugh and a daughter Bertha. His son was barred from legitimate succession since the pope did not recognize Lothaire's second marriage, which produced Hugh. Hugh became a contestant for control of his father's territory, against Louis the German and Charles the Bald who wanted to divide it between themselves. Later, Hugh allied himself with the Viking Godorid, who settled in Frisia, against Charles the Fat. Hugh was captured by Henry of Babenberg on behalf of Charles the Fat and blinded.

AR denier, 17mm, 1.1gr. Obv: +LVDOVVICVS INP, central cross over lines. Rev: +ANGILBERGA NP, central cross with eight rays. Mint is Benevent (It). R2013; MG 1178; Dep 10-F1, 141M (8 examples); MEC 1116; not in Prou.

Louis II received Italy. He died in 875, also without an heir. His daughter married Boso of Provence who rebelled at the end of the reign of Charles the Bald. After Charles' death he established himself as king of Provence. He died in 887, and was ultimately succeeded by his son, Louis the Blind.

AR denier, 22mm, 1.47gr. Obv: +CARLVS REX, central cross. Rev: +ARELA CIVIS, central monogram. Mint is Arles. Dep 13-01, 69 (14 examples). MG 1423 as Charles III; Prou 862 as Charles le Gros (roi) same years; R lists 1269 as Charles of Provence but there is no coin image matching this number. Not in MEC, Bel and Nouchy. The more common Charles le Gros from Arles is CARLVS IMP. This is clearly a coin with variable attribution.

The third son, Charles of Provence received Provence. Charles of Provence was not a healthy person and died in 863. After his death his lands were split between his brothers, Lothaire II getting the northern section and the south going to Louis II of Italy.

This branch of the family died out with Louis II's death and there was no direct Carolingian heir to assume authority here. Provence essentially broke away and established itself as an independent kingdom for a time, under Boso, whose Carolingian connection was via marriage.

II: Louis the German died just before Charles the Bald, in 876. He was a one time ally of Charles the Bald but after the death of Lothaire II, contested with Charles over the split of Lotharingia. He had three sons, Louis (the Younger)  III , Carloman of Bavaria and Charles (the Fat) III.

Carloman of Bavaria died in 880. Louis the Younger died in 882. While not yet a possible ruler at this time, Louis the Younger's young son died falling out a palace window, depriving him of an heir.

AR denier, 21mm, 1.50gr. Obv: +CARLVS IMP AVG, central cross. Rev: +BITVRICESCIVI, central monogram. Mint is Bourges. R 1564. Roberts says "coins inscribed CARLVS IMP Rex can be attributed" to either. He notes Grierson assigns most to Charles the Bald, Crinon gives the southern mints to Charles the Fat. MG 1485 classifies this as a 'late 9th coin of an emperor Charles," arguing for indeterminacy. Dep 198 (801 examples) and notes "Les monnaies de Charles le Chauve de tresor de Rennes ont ete attribuees a Charles le Gros par J. Lafaurie, en raison de leur faible poids. Grierson (MEC p.235) refuse cette hypothese, attribuant ces monnaies a un imitatuer local. (p.120)" MEC 917; Belaubre 176 attributes this to Charles le Gros.

Charles (the Fat) III was deposed by his nephew, Arnulf the bastard son of Carloman of Bavaria, in 887 and died in 888. Arnulf lacked the authority of a legitimate Carolingian and gave significant power to key lords to maintain his own titular authority. On the other hand, he was the only direct line Carolingian male ruling by 887.

With Charles (the Fat) III's death this branch of the family effectively ceased to be major players in Francia and the west during this period of turmoil.

III: Pippin I, the third of Louis the Pious' sons, died in 838. He was succeeded by his son, Pippin II, who spent much of his life in conflict with Charles the Bald since Charles' inheritance was cut out of territory originally given Pippin I. Pippin II died in 864 without an heir.

Pippin I (814-838) or Pippin II (840-52)

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AR denier, 21mm, 1.61gr. Obv: +PIPINVS REX EQ, central cross in solid circle. Rev: +METVLLO, central Pippin monogram P-IN-S-R. Mint is Melle. R1872, MG 606 as Pippin I or II; Dep 9F1, 615 (33 examples), "les tres grande majorite des monnaies de Pippin II fut frappe entre 845-848 ... Melle fut un atelier tres important." This coin is conservative in design, following Charlemagne's lead with the ruler's name on the obverse and a personal monogram on the reverse. MEC 814; Prou 689;  not in Bel.

This branch of the family had no male heirs after Pippin II's death in 864.

IV: Charles the Bald was the youngest son of Louis the Pious and his last surviving son. He died unexpectedly in 877. He was in Italy for his wife's coronation as empress when he learned of an army marching on him in Italy, lead by Carloman, son of Louis the German. He also learned he was facing a revolt at home, involving Boso of Provence, Hugh the Abbot, and others, possibly including his primary heir Louis the Stammerer. He re-crossed into France via Mont Cenis. He fell ill and died at Avrieux. He was 54.

AR denier, 20mm, 1.69gr. Obv: +GRATIA D-I REX, central KRLS monogram. Rev: +SC-I qVINTINI MO, central cross. Mint is St. Quentin. R1495v; Dep 11-A1, 906v (120 examples). 906 ends in MONET. MG 772; Prou 249; MEC 899.

Charles, in turn had three sons, but two of them predeceased him. Charles the Child died in 866 and Carloman, an abbot, died in 876. His heir was Louis (the Stammerer) II.

AR denier, 21mm, 1.4 gr. Obv: +MISERICORDIA DI REX, central Lvdovicvs monogram. Rev: +TVRONES CIVITAS, central cross. Mint is Tours. R1608 as Louis II or III; MG 1255 as Louis II or III; Dep 13 F1, 1041v (cites DEI, 121 examples) as Louis III; Prou 453-58 as Louis II or III; MEC 967 as L III; Nouchy Louis III #4.

Louis the Stammerer was crowned at Compeigne in 877.  However, his reign was short. He tried to come to terms with his Carolingian cousins and he met with Louis the Younger, son of Louis the German. However, he faced revolts and never made a comprehensive peace. He became ill and died two years after his coronation, in 879. He was only 33.

He had three sons; Louis III, Carloman and Charles (the Simple) III.

AR denier, 20mm, 1.55gr. Obv: +KARL CT IO, central Rx. Rev: MONT S NAZ, central cross. Mint is the church of St. Nazaire in Autun. R-; Dep 94 (9 examples). He cites the legend as +KARL CT D and MON +S NAZ. MG 1419 as Charles III; Prou 603 as Charles III; PdA 5638 (which matches this legend but is without attribution); MEC as Charles the Bald. They cite this as a unique style of CB and date it from a hoard. There is no other CB coin with the Rx. I'm skeptical.

Louis III was crowned at Ferrieres in 879 and ruled over Neustria for three years before he died in 882. He was only 19 when he died of the consequences of a riding injury. From Nelson; Louis died "of internal injuries incurred 'chasing a young woman on his horse for his  joke (sic) (for he was a young man)'.."

Carloman, brother of Louis III was crowned at the same time. He received Aquitaine and Burgundy but reigned for only five years before he died in 884. He died of a leg wound at the age of seventeen years. Again from Nelson; he died "after being accidentally wounded in the thigh by one of his companions while hunting with young men."

Louis the Stammerer's third son was only a child of five and too young to rule. He ultimately was named Eudes' heir and ruled as Charles III.

Here's a recapitulation of this grim period for the Carolingians where death took such a heavy toll. Boso of Provence, not direct line but linked by marriage and a potentially strong ruler died in 887.

Louis II of Italy, son of Lothaire I: 875
Louis the German: 876
His son Carloman: 880
Another  son Louis the Younger: 882
Another son Louis the Fat: deposed 887, died 888
Charles the Bald: 877
His son abbot Carloman: 876
His son Louis the Stammerer: 879
Louis III: son of Louis the Stammerer: 882
Carloman, son of Louis the Stammerer: 884
Boso of Provence: 887

In contrast to this concentration of Carolingian direct line male deaths, the experience was gentler from the death of Louis the Pious until 875. Whereas there were 10 direct line heir deaths in the thirteen years from 875 - 888, there were only six in the previous 35 years, between 840 - 875.

Louis the Pious: 840
Lothaire I: 855
Charles of Provence, son of Lothaire I: 863
Pippin II, son of Pippin I: 864
Charles the Child, son of Charles the Bald: 866
Lothaire II, son of Lothaire I: 869

Who was left in a direct male line by 887?

Arnulf, bastard of Carloman in the line of Louis the German
Hugh, blinded bastard of Lothaire II in the line of Lothaire I
Charles III, five year old son of Louis the Stammerer, line of Charles the Bald

Premature death had wreaked profound havoc on Carolingian prospects for continuity. By the time Charles III became king after the death of Eudes in 898 the Carolingian empire had unraveled and been replaced by a series of local and relatively weak kingdoms.

Francia did not have the luxury of waiting for the maturity of a direct Carolingian heir. Internal rebels, such as Boso in Provence, quickly moved in to fill the power vacuum left by the absence of a Carolingian heir. Simultaneously, external threats, primarily but not exclusively in the form of Viking incursions, meant that territories in the former empire had to look for strong and local leadership to provide protection. Without Carolingian candidates, central control eroded and local lords took advantage of the situation. One hundred years later, when the Capetians came to power, French kings had to start the long and difficult process of bringing now strong feudal families under royal control.

Sources:

Nelson, J., Charles the Bald

Riche, P.,  The Carolingians

* Codex image from the University of Delaware