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I don't think it can be said that there was colonisation in Tibet and Xinjiang, until very recenly, and then, there is also a fast growth of chinese communities in the Russian Far East.
There was actually a very systematic process of colonization in Xinjiang that began in the Western Han around 100 BCE. Several colonies were set in Lun Tai, and served as a rest stop for Han armes and envoys. Several posts were then created later; the protector general, the Mao Yi Xiao Wei(in charge of agriculture), and the Xi Yu Zhang Shi. The Former Liang was the first to turn Turfan into a Commandery, and the Tang also made Turfan into a prefecture. The rest of xinjiang was not directly incorporated into the bureaucratic administration, but were supervised by agricultural colonies and garrisons near them.
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Han and Tang expeditionary armies were able to go deep into the steppe and inflict heavy damage on nomadic empires, driving the nomads to retreat westwards or northwards. But holding the captured steppe territory with forts or cities and garrisons would have been extremely expensive, since the soil is not suited to farming and any supplies have to be transported from a long distance away. The nomadic empires didn't have this problem because their control of the steppe was not based on territory but rather on securing and retaining the loyalty of the tribes who used that territory for herding. That is why the Eastern Han and Tang empires could only exert some control over the steppe indirectly through Xianbi and Tiele tribes that were allied to them (or officially vassals of the emperor).
Interestingly, the Yuan was the first dynasty which colonized Mongolia by establishing a military garrison in Karakorum. As Arthur Waldron points out, if a China based regime really wants to spent its resource to control the nomads, they could do it and the Yuan is a great example. Yet the Ming resorted to the old Chinese mentality of securing China first instead of wasting resources on the steppe. Even though Hong Wu established 8 garrisons in inner Mongolia, Zhu Di withdrew most of them.
Other than the Yuan, the Han was the first dynasty which made the attempt to turn Outer Mongolia into a province, when the Xiongnu rebelled in 10 AD Wang Mang declared that their entire state be made into a province and mustered a force of 300,000 to march north and destroy them. But before that army could move, rebellion broke out and the entire army disintegrated. The Tang did make Outer Mongolia into a jimi protectorate, briefly establishing the pacified north protectorate in Otugen, capital of the former Tujue empire, and even established a road that channeled the place with Chang An where Tang envoys would be sent north of the Gobi periodically to collect tribute. The Qing dynasty was the most successful regime in regards to the control of Mongolia. It zoned the entire region into banners and forbid each tribe to move beyond their designated banner. The Qing's success might have a lot to do with the changing social structure of Mongolia itself when Lamaism was introduced.
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The case of Manchuria is a little different from the steppe. From the Liaodong region one has two possible directions in which to expand: northwards into the northeastern plain of Jilin and Heilongjiang, or eastwards into north Korea. Both areas have arable land suited to agrarian settlement, but for some reason, the Western Han, Sui, and Tang empires chose to expand only into Korea. I am not sure why; maybe someone could offer an explanation?
Manchuria might have some arable lands, but they are far too few. Jilin and Heilongjiang have lots of woodlands and wetlands. They are also too cold for any large amount of farmlands. Other than a few population centers, like in Haerbing and Mudang river, most of the vast territory of these two provinces were uninhabited. It wasn't until the Jin that heilongjiang gained any significance in international politics. Dynasties prior to that might have simply neglected it because it was not worth the effort.