In 1683, following a naval engagement with Admiral Shi Lang, one of Koxinga's father's trusted friends, Koxinga's grandson Zheng Keshuang submitted to Qing Dynasty control.

Despite the expense of the military and diplomatic campaign that brought Taiwan into the imperial realm, the general sentiment in Beijing was ambivalent. The point of the campaign had been to destroy the Zheng-family regime, not to conquer the island. Qing Emperor Kangxi expressed the sentiment that Taiwan was "the size of a pellet; taking it is no gain; not taking it is no loss" (彈丸之地。得之無所加，不得無所損). His ministers counseled that the island was "a ball of mud beyond the sea, adding nothing to the breadth of China" (海外泥丸，不足為中國加廣), and advocated removing all the Chinese to the mainland and abandoning the island. It was only the campaigning of admiral Shi Lang and other supporters that convinced the Emperor not to abandon Taiwan. (Guo 2003) Koxinga's followers were forced to depart from Taiwan to the more unpleasant parts of Qing controlled land. By 1682 there were only 7000 Chinese left on Taiwan as they had intermarried with aboriginal women and had property in Taiwan. The Koxinga reign had continued the tax systems of the Dutch, established schools and religious temples.

Reference

http://en.wikipedia.org/wiki/History_of_Taiwan