The Tibetan Empire emerged in the 7th century, but with the fall of the empire the region soon divided into a variety of territories. The bulk of western and central Tibet (Ü-Tsang) was often at least nominally unified under a series of Tibetan governments in Lhasa, Shigatse, or nearby locations; these governments were at various times under Mongol and Chinese overlordship. The eastern regions of Kham and Amdo often maintained a more decentralized indigenous political structure, being divided among a number of small principalities and tribal groups, while also often falling more directly under Chinese rule after the Battle of Chamdo; most of this area was eventually incorporated into the Chinese provinces of Sichuan and Qinghai. The current borders of Tibet were generally established in the 18th century.
Try to answer this question if possible (otherwise reply "unanswerable"): Which battle left parts of Tibet under Chinese rule?
Battle of Chamdo