Angry Bear has a nice summary of the redistricting battle of 2001 and how it wound up in the federal court. His conclusion:

The net result of this was that the panel adopted the original plan proposed by the Texas Senate, which was identical to the Texas House version, but without the Spanish surname gerrymandering. [...] So at the end of the day, the adopted districts were drawn by Republicans.

UPDATE: Angry Bear has some corrections to his original post describing how the current boundaries were drawn.