Well, the term seemed to the legislature less ethically offensive than “rent-a-judge”, which is another way to reference the concept. Actually, to serve as a special judge under Chapter 151, CPRC, the judge, (former or retired), must have; (1) served as a judge for at least 4 years in a district court, statutory county court, statutory probate court, or appellate court; (2) developed substantial experience in the judge’s area of specialty; (3) not been removed from office or resigned while under investigation for discipline or removal and (4) annually demonstrated completion in the past calendar year of at least 5 days of continuing legal education in courses approved by the state bar or the supreme court.
Whether that makes them “special” is a matter of opinion. However, unlike an arbitrator, it is much easier to vet the qualifications, temperament, knowledge, experience, proclivities, etc. of such judges by talking to lawyers who have practiced in their court. State Bar polls may also be of some use as well as reports of reversals. A simple computer search could tell you a lot. When the parties have agreed on a judge, they simply call him/her, check conflicts, schedule and agree on a price.
ONCE WE HAVE THE JUDGE IN MIND, HOW DO WE START THE PROCESS?
The statute applies only to civil or family matters that are filed in a state district court, statutory probate court or statutory county court. The lawyers simply file an agreed motion for referral that agrees to waive a jury trial, states the issues to be referred, sets the time and place for the trial and identifies the judge who has agreed to hear the case and how much the judge is to be paid.. The case is referred to the special judge and the referring, (sitting), judge never has to deal with it again, (unless the special judge fails to render his “verdict” within 60 days following the trial’s adjournment. ) Perhaps the best news of all- the rules and statutes relating to procedure and evidence in the referring judge’s court apply. The case is tried non-jury and the trial may not be held in a public courtroom unless ordered by the referring judge.  When the special judge renders a decision, (called a “verdict”), the parties simply take it to the referring judge to perform the ministerial task of entering a judgment on the special verdict. The referring judge need not “confirm” the verdict nor is the court empowered to change it. Any challenge to the now entered judgment goes straight into the appellate system as provided by the Texas Rules of Civil Procedure and the Texas Rules of Appellate Procedure.
WHAT ABOUT THE COST?
To begin with, there are no “administrative fees” associated with this procedure, which can be significant in arbitration matters. The special judge is paid pursuant to the parties’ agreement and that amount is disclosed in the agreed motion for referral. The parties must pay, “in equal shares”, the special judge’s fee, and the court reporter’s fee. Costs associated only with a single party’s case, included witnesses, are borne by that party.
Arbitration Horror Story No. 302
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 CPRC Sec. 151.001
 CPRC Sec. 151.002
 CPRC Sec. 151.011
 CPRC Sec. 151.005
 CPRC Sec. 151.010
 CPRC Sec. 151.013
 There is a reference in CPRC Sec. 151.009(2) to sharing of “administrative costs” but those refer to minor matters more akin to “costs of court”.
 CPRC Sec. 151.009