Unless it is at the specific request of the Defendent because of extenuating circumstances (like wanting or not wanting to use the same PD as last time), Judges are not allowed to be involved in the appointment of PDs in our state (at least in the counties I have personal knowledge of).
The Clerk of the Court is the one who handles the appointment of PDs and it's done on a rotational basis...who is ever next on the list of Deliquency cases or the next three on the list for Dependancy cases. And the only reason allowable for the Clerk to "jump" an attorney is at their personal request...like they are on vacation or they already have a heavy caseload.