For this summary I have drawn on Sharifuddin's History of Timur Bec " in the English version, a good though too eulogistic account: somewhat long however and not easily obtained. Throughout I have used freely Manger's annotated Latin version of Ibn Arabshah.
After Timur's death his issue strove for power and before long Shah Rukh gained the empire. He ruled with success until A.D. 1447, when he died and was succeeded by his son, Ulugh Beg, who was murdered two years later. However he had already achieved fame as a patron of architecture and astronomy. After his death the dynasty declined, though another line descended from Timur gained power in India.
Samarkand is now the capital of the Uzbek Soviet Republic and a town of some activity. The Muslim city is still beautified by colleges and other buildings of the time of Timur and his successors, but his own tomb is half in ruins.

Mughal Library