Oh but there was! It was just extremely unstable. Much like the rest of post-Carolingian Europe, Carolingian Italy too was run by a group of "Margraves" whose office quickly became dynastic after the Emperor's death. The title of King of Italy rapidly became contested in a convoluted back-and-forth between the Guideschi, a dynastic party from the rugged highlands of Central Italy, the Aleramici, hailing from the hummocky western foothills of the Alps, and the Unruochings, from the northeastern border march of Friuli.

However, what had been the heartland of Lombard Italy prior to Charlemagne's conquest never really bought into the carolingian system. Characterized by a complex hydrography consisting a series of parallel waterways flowing down the Alps across a broad plain to the river Po, "Lombardy" was a densely populated and urbanized region. Curiously, it had been largely absent from the near-endemic civil strife that had catarterized post-Carolingian Italy.

Lombardy too had been assigned a Margrave whose became dynastic. However, this dynasty, the Obertenghi, were surprisingly passive. It's important to understand that the densely populated and urbanized heartlands of the Po basin sustained a stable (some would argue growing) population living in cities, where only with difficulty authority could be concentrated in the hands of a single person. Royal representatives and margraves alike had to contend with clergymen, judges, and lawmakers seated in the cities who were elected, in the Roman fashion, by colleges of prominent citizens. Indeed, thousands of large and medium sized landowners split their time between country estates and urban residences, while small farmers, aided by the shallow waterways crossing the plain and a weak legal precedent for obligations to their landlord, regularly traveled to town in order to bring their goods to market and purchase finished goods made by urban artisans. All this contributed to the liveliness and bustle of urban life. This led to a paradoxical situation where if we consider there was anarchy in the border marches where single strongmen reigned supreme, in the the urban heartland where no one person was unquestionably in charge there was law, order, and some degree of prosperity.

Thus, many generalist histories tent to ignore the, admittedly convoluted, dynastic conflicts between the Guideschi, Aleramici, and Unruochings (with guest appearances by the Kingdom of Burgundy) and instead focus on the developing political, social, and economic characteristics of the Po basin. The urban political system, the embryo of the Communal Government that would emerge the next centuries, is the only system acknowledged and retained by Kaiser Otto when he enters Italy halfway through the tenth century. Part of his considerations were political; he set out to undermine and destroy the great dynastic powers of Italy, however it's certain that practical concerns also determined his decision on what to replace these powerbroker with; partially mirroring what he had instituted in Germany, where he ruled by traveling around the country with a retinue of scribes and administrators who would link up with local clergymen in order to govern.

The above is, of course, a cursory overview. Was there anything particular about the post-Carolingian succession you were wondering or confused about?