For much of its history, China has seen itself as the geographic and cultural center of the world. Until just a few centuries ago, China referred to itself as "The Middle Kingdom," a term which betrayed its ethnocentrism. This national pride may have been largely deserved, however, because many of China's neighbors were more than willing to acknowledge China's cultural greatness. In fact, Japan and Southeast Asia when to great lengths to imitate everything they could about Chinese culture and the Chinese way of doing things.
Japan borrowed much from China including its culture, religions, and political structure. Despite the best efforts of the aristocracy, however, Japan could never manage to simply copy China with its expansive imperial bureaucracy. Geography was a major impediment to this. The Islands of Japan were separated from each other by water and even the settlements on each island were separated from each other by mountains. Thus, local governments proved more important than they did in China.
Also, because geography necessitated that the local "daimyo" share much of the responsibility for administering their territories, they retrained more power than a local ruler would have had in China. Simply put, Japan was different than China, so Chinese culture took a different form there. The same thing can be seen today. Americans export their culture all over the world, yet those parts of the world that embrace it always have their own unique take on it.
Its proximity to China meant that certain parts of southeast Asia borrowed a great deal from the Middle Kingdom. Especially in Vietnam, Chinese religion, culture, and political ideas took root. This cultural exchange was due, in part, to the great amount of trade that took place between the two regions. China imported many goods from Southeast Asia, and Southeast Asia, in turn, imported goods from China for themselves and to trade with others. In fact, Southeast Asia did a great deal of trade with people from other regions too, which explains why Southeast Asia was not simply "another China" further south.
True, Southeast Asia borrowed a great many things from China, but it also borrowed things from India and the Islamic world. Large portions of Southeast Asia even converted to Islam and Hinduism. Obviously, this undermined the Chinese influence in the region. We may think of early modern Southeast Asia as a "cosmopolitan" area. It embraced differing ideas, but this also meant that no single creed, including that of China, could dominate there.
