Final answer:
Charlemagne's empire was governed locally by counts who oversaw counties and margraves who ruled border regions known as marches. They acted as representatives of Charlemagne's authority, although rebellions were frequent, requiring his intervention to maintain control.
Step-by-step explanation:
The officials who ruled parts of the empire under Charlemagne's name were referred to as counts and margraves. Charlemagne organized his vast territories into counties, each overseen by a count, typically his military followers or sometimes commoners. These officials were appointed to rule lands where they had no personal ties, serving as the local authority representing Charlemagne's interests. To protect the borders, lands called marches were established and governed by margraves, who were military leaders tasked with defending against foreign invasions. Furthermore, Charlemagne deployed a group of royal officials, sometimes known as missi dominici, who traveled throughout the empire to inspect the administration of the counties and marches and ensure loyalty to the emperor.
Despite Charlemagne's efforts to maintain control, rebellions were not uncommon, and the emperor frequently had to suppress insurrections to reaffirm his authority.