Is there a list of Capital Punishment Qualified Defense Attorneys in some central location?

Or does each District take care of its own list IAW 26.052?

I am not sure if you're asking about local lists, administrative region lists, or a state-wide list. As far as I know there is no state-wide list.

Otherwise, if there is no public defender, a list of qualified attorneys should be maintained in the administrative judicial region. See TEX. CODE CRIM. PROC. art. 26.052 (c). The administrative judge of the region is responsible for appointing a selection committee to set the standards and approve the attorneys who are competent to act as lead counsel in a capital case. The list should be posted prominently in the district clerk's office of all qualified attorneys in the region. The procedure is relatively new, having been created as part of the Texas Fair Defense Act in 2001 (before that the procedure was less complicated).

Typically, I believe, the administrative judge of each county forwards the names of the defense attorneys who apply to the regional administrative judge for further approval. I've found the staff attorneys who work for the administrative region particularly helpful in helping to understand the procedures in practice. I've looked into this area pretty recently, so feel free to contact me if you have any more specific questions.

A local list of qualified trial attorneys for capital cases is supposed to be kept in each of the nine administrative judicial regions in the state, and the minimum qualifications for those attorneys is supposed to be posted in each district clerk's office in the state.

A statewide list of qualified habeas attorneys for capital cases is kept by the Court of Criminal Appeals.

You might also contact the State Task Force on Indigent Defense here: The Link