How much of the Gokturk empire did the Tang occupy

 

 

Most of it. The only part of the Turkish Empire which the Tang state didn't occupy was the Khazars in southern Russia. Below is a map of the Tang at the height of its expansion in 669 made by Tang Qixiang. Tang Qixiang's map series are the most authoritative map of Chinese historical empires at the moment since it consulted a large amount of primary source material to derive its conclusion.

 

 

 

 

 

 

Below is a Japanese historical publication of the Tang empire in 668 after including all of its vassals such as the Tuyuhun and Silla:

 

 

 

After the Tang occupied the Eastern Gokturk Empire in 630, it divided what is today Inner Mongolia into two prefectures and the rest of the tribes north of the Gobi in what is today Mongolia and Siberia were under the control of the Xueyantuo Khanate. The Tang destroyed this khanate in 647 and divided its territory into six prefectures and seven protectorates, two more prefectures were added in 649 when the Guligan north of lake baikal submitted. This marked the northern most extension of Tang power.

 

 

The western most extension of Tang power was achieved after 657 when the Tang army destroyed the Western Turkish Khanate and Tang power reached all the way to Sigistan on the border of Iran. The territory of present day Afghanistan was made into the Tuhuoluo protectorate and it was possible that Tang prefecture generals were established there too. This control was short lived and ended in the 670s when the Tibetans and Arabs, along with Turkish rebellion cut off communications between these regions and China.

The Tang already lost its Mongolian possession in 686 after the Later Gokturks declared their independence in 682 and conquered the tribes north of the Gobi under Tang control in 686.

 

 

Even the map you've shown for 750 has a few mistakes; the Ordos region was still part of the Tang empire in 750, just not a prefecture; it still had three fortresses known as Shouxiang city on the northern bank of the Ordos. The Kingdom of Nanzhao and parts of Manchuria were all parts of the Tang prefectural system. Below is a more complete map of the Tang in 741 also made by TanQixiang, the most authoratative map historian in china: