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By the time that Qin had totally collapsed, Xiang Yu was China's hegemon. He allotted governance of different parts of the country to various men. Some, like Tian An of Qi and Wei Bao of Wei, were descendents of the prior kings of those areas, while people like Wu Rui of Hengshan were given their posts based upon distinction. All of them had full control of their own forces and were largely free to pursue their own policies.
Liu Bang was one of these kings, and some of the others submitted to him in the fight against Xiang Yu. Liu Bang also relied upon three key generals - Han Xin, Peng Yue and Qing Bu - each of whom were promised the position of king as the condition for their assistance. Thus, at the formation of Han, Liu Bang found his territory full of kings who commanded the loyalty of their forces and expected a great deal of autonomy as reward for their services. While he had his own military force (the conscript Southern Army and the professional Northern Army, both based in Changan) and could theoretically command the kings as he pleased, the size of their territories made practical enforcement of this difficult. As Qing Bu demonstrated, it was quite feasible for a king to revolt and be a genuine threat to the empire. Liu Bang therefore spent a lot of time removing the various kings (either by plots or putting down rebellions) and replacing them with his relatives (Wu Rui was eventually the only non-relative king remaining).
Even with relatives in charge, the central government could be at the mercy of the kings, as demonstrated by the rebellion of seven kings under the reign of Emperor Jing. One of the responses to this was an imperial decree that territory should be split up between a king's sons rather than passing in full to a single heir, announced with the excuse that the Emperor was acting out of kindness to all princes but really intended to dilute the power of kings and limit their ability to threaten the Emperor.
Another was the establishment of commanderies in locations that inhibited the kings' ability to cooperate. Commanderies had existed from the start of Han and were headed by centrally appointed officials. Initially, many commanderies were near the capital Changan, but as time passed, they were established also in strategic locations such as between potentially troublesome kings and along the empire's frontiers.
A key part of the power of Liu Pi, the leader of this rebellion, was his ability to mint his own coins and the abundant ore available to do so from his territory. Eventually, this power was removed and all minting of currency was done within three central offices (there were still counterfeit coins, but they couldn't be made on a scale that could sustain a rebellion).
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The Han Dynasty came after the Qin Dyansty, after the government under Shi Huang Di collapsed. Liu Bang is noted as coming from a peasant family and becoming the Han Emperor, about this time there are many books and lots of material to look at. Still during this time China established the Confucian System, which began the Imperial Academies to train those who wanted to enter government, this also opened China to some international trade and during this period Buddhism entered China from India during the time of trade and the creation of the Silk Road.
The government was fairly unified, but as during most periods of China you have various levels where the Imperial Government sits on top and dominates, then you have various local levels of control. The Imperial edict is generally respected, after all it comes from the Emperor, which allows lower level officials to work within the system created. There is an army that protects the country, but using marriage as a way to unify and create diplomatic ties to other countries you have ties of politics and blood.
The Han period was also a technological period as well, where China began to develop some of the technological expertise it became known for.
There are many World History sites that refer to the Han overall, including a PDF link that overall goes into how the Imperial soldiers (central army) were in compulsory service, trained and paid. There are periods when China did have lords who provided soldiers, but most of my recollections on that comes from later periods and not this early.
Really to go into more I'd have to get some books together, but this should be a good start.