when did the city-states of the Tarim Basin became Uyghur?

[Temüjin]

nowadays the city states of the Tarim Basin are Uyghur speaking, though according to the maps by Yuri Bregel in his book, it seems that they Uyghur Khanate and subsequent Uyghur Idiqut state centered at Qocho never seem to have controlled the westerna nd southern part of the state. so i wonder when exactly did those city states adopt the Uyghur language? was it during the Chaghatai Khanate or did in fact the Uyghurs adopt the language spoken by the city states (Jagatay?) and is today called the Uyghur language, similar to what happened in Mawarannahr/Uzbekistan?

[H. İhsan Erkoç]

After the fall of the Orkhon Uyghur Qaghanate in 840, the Uyghurs settled on the northern part of the Tarim Basin (the "Beilu" or "Northern Path" as called by the Chinese). This Uyghur kingdom was centered at Qocho (Turfan) and ruled all the lands up to Kashghar, but Kashghar was never a part of this kingdom. In fact, the Yaghma tribe, which was a member of the Uyghur union before 840, settled in Kashghar following the Uyghur migration to the Tarim Basin and it was from these that most probably the Qarakhanids descended. The cities under the rule of the kingdoms of both Qocho and Kashghar were quickly Turkified during the 9th century and the Tokharian languages soon disappeared. However, the southern half of the Tarim Basin (the "Nanlu" or "Southern Path" of the Chinese sources), centered on the Kingdom of Khotan (which was inhabited by an Iranic people), remained independent and non-Turkic well up to the early 11th century, when it was finally conquered by the Muslim Qarakhanids. Khotan was the last area of the Tarim Basin to be Turkified; the spread of Islam in Tarm Basin, however, was far slower compared with the spread of Turkification. The mostly-Buddhist Qocho Uyghurs resisted Muslim Qarakhanids and they were never conquered by this Muslim dynasty. It was at a far later date, during the later years of the Chaghataid period, when these Uyghurs were finally Islamised (during the 14th-15th centuries IIRC). As for the language; "Khaqani Turkic" or the written language of the Qarakhanids was actually almost the same with Uyghur of the same time except very few local differences. The Qarakhanids and Uyghurs shared the same dialect and the same life style, representing a sedentary and literate Turkic culture opposed to the nomadic Turkic culture which used writing on a much smaller scale. And the Chaghatai dialect evolved later from the Khaqani/Qarakhanid dialect.