Just gave this a cursory test, and civ capitol improvement doesn't move at all. Gave Earth to the Drengin, and my new capitol had a initial colony building, not a civ capitol. Took Earth back, and it still had the civ capitol building, but wasn't my capitol. Also, the set as homeworld button was grayed out, meaning I never even got the option of changing my homeworld.
I know damn well that AI's don't get that benefit. I take their capitol, it still has the civ capitol building even when I own it.. I take whatever world they moved their capitol to, it has an initial colony building, not a civ capitol.
I seem to recall this being changed early in DA, as people were using this as an exploit. What version are you running, fistleaf?
*edit* The set homeworld button is a holdover from earlier versions, I can't remember the last time I saw it functional.