By the time of the last days of the Han Dynasty, the hundred-or-so Commandaries of the Empire were subdivided into around 1200 Counties. This was the smallest administrative level lead by an official appointed directly by the Han court. A typical County would consist of a large town or city which would act as the local capital and centre of governance, and the surrounding region and countryside. Counties would then be subdivided even further into smaller cities, towns and areas of concentrated population within the region, known as Districts. These would then further be split down by the Han bureaucracy into smaller villages, groups of families, rural communities, estates and the like, until you get as far down as individual households.
Getting too in depth about anything lower down the bureaucratic pyramid than the county level would be untenable, especially for the scope of this quest. Still, given Liang Shu's adventures thus far have focused mostly on the county level, it might be worth digging a little deeper.
The Prefect
Prefects were noted for being the lowest ranking officials in a local administration that were assigned directly by the central government in Luoyang. As head of the county government, they had a rather considerable number of responsibilities, as well as a surprisingly large amount of executive authority and autonomy, provided they were only dealing with matters within their jurisdiction. Functionally, they can be seen as a city mayor, chief of police, head judge and priest all in one. Among other duties, they were expected to store grain and manage harvests, supervising public work projects, ensuring peace and order, enforcing the laws of the Han, acting as judge in criminal cases, promoting men of talent to positions within the county, surveying and interviewing the civilians, performing religious ceremonies and sacrifices, mobilising local corvee labour, registering property and more. They themselves would take order and direction from the Grand Administrators, who would play the role of both overseer and director for happenings for each county in their commandery. Salary rank for a Prefect would vary depending on the population of their county. The more registered households of Han Chinese families, the higher the Prefect's salary. In more populated Counties, a Prefect's salary rank could be equal to (or easily exceed) that of a Provincial Inspector, which easily shows just how many responsibilities were thrust upon them. After a harvest and before New Year, the Prefects were expected to give full reports to their commandary's Grand Administrator, detailing a population census, status of cultivated farmland, degree of collected taxes, local law, order and stability, and a full account of the county expenditures. Many Prefects would find themselves woefully unprepared for their job (especially if they bought their position, a practise common around the end of the Han) and would often have to learn fast. As a Prefect could appoint his own staff, cronyism among his ranks could certainly happen, especially when oversight got more and more lax around the last years of the Later Han. Under him, the Prefect would have a myriad of aides, clerks, secretaries, guard captains, libationers, judges and a Master of Records, of various ranks.
The County Assistant
The right hand man of the Prefect, the County Assistant would help him in his otherwise daunting task. He would serve as the Prefect's adviser, as well as being a liason with local gentry, nobility and elites. They would act as bookkeepers, record makers, and would be in charge of official documents and legal nuances. As part of his aid, he would oversee the granaries and food storage and offer expertise in legal matters. Should the Prefect fall ill, be incapacitated or otherwise be unable to carry out his role, the County Assistant would be expected to fill in. His own salary would scale based on the Prefect's - so a County Assistant in a county with a larger population would earn more. Counties with very large populations would have an additional County Assistant, whilst the the Prefect of Luoyang, the capital of the Empire, would have three. Assistants would have his own small staff and offices to aid in his endeavours.
The County Commandant
The County Commandant would earn an equal rank to the County Assistant, again scaling based on the population, and would serve as the left hand of the Prefect. The Commandant would be charge of local policing and law enforcement. He would head the guard captains and ensure the security of the county. Troubled counties or those on the frontier would have at least two Commandants, whilst counties home to very large cities such as Chang'an could have up to four. They would have the responsibility of gathering up militia and snuffing out banditry and keeping the roads safe, as well as keeping an eye on clans or tribes within the county who may be hostile to the Han government. Under his command, the Commandant would have several Patrol Leaders, entrusted with militia and local volunteers to man watchtowers, guardposts and gatehouses. Whilst in charge of military affairs in times of peril, the Commandant would will defer to the Prefect as superior. In addition, in times of real peril or upheaval, the County Commandant would often find himself subordinate to officers of the Grand Administrator, or even military officers sent by the state government if things were truly out of hand. Counties along the far northern frontier would also have a County Commandant of Fortifications, whose role was to aid in the defences of the border posts and walls of the Han Empire, and assist in raising levies against nomadic incursions.
The County Bureaus
To administrate a county, the Prefect would be aided by various Bureaus based in the county capital city. Each of these offices would be a mini bureaucracy in its own right, lead by a Division Head and each with a network of staff of various ranks and importance underneath. These would almost all be made up of men from the local county, and it would be among the Prefect's responsibilities to ensure each Bureau would be staffed by the able and trustworthy. Each county would have a Bureau of All Purposes, a "catch all" office. Its duties would include inspecting the various settlements and villages in the outlying county, encouraging and directing agriculture and farming, liaising with gentry and their estates, and encouraging local festivities and religious rituals. Other common Bureaus would include Banditry, Arms, Households, Laws, Granaries, Markets, Consultations, and Gatherings.
The amount of Bureaus would depend on both a county's size and needs. There were many who would depend on the resources and specific requirements a region might have. For example, a county with bountiful iron ore deposits would likely have a Bureau of Metal, whilst a county undergoing significant construction would have a Bureau of Architecture.
As mentioned earlier, each county was then divided even further into districts, which would be subdivided into an even smaller level - with each also having an increasingly large number of officials and clerks and other government staff. However, getting into the nitty gritty of how, for example, a single city block or outlying village was administered and ran is a bit beyond the scope of this broad overview.