California Civil Procedure Code
In addition to the circumstances referred to under Article 4 (commencing with Section 1297.131) and Article 5 (commencing with Section 1297.141) of this chapter, the mandate of an arbitrator terminates upon his or her withdrawal from office for any reason, or by or pursuant to agreement of the parties.
Where the mandate of an arbitrator terminates, a substitute arbitrator shall be appointed according to the rules that were applicable to the appointment of the arbitrator being replaced.
Unless otherwise agreed by the parties: (a) Where the sole or presiding arbitrator is replaced, any hearings previously held shall be repeated.
(b) Where an arbitrator other than the sole or presiding arbitrator is replaced, any hearings previously held may be repeated at the discretion of the arbitral tribunal.
Unless otherwise agreed by the parties, an order or ruling of the arbitral tribunal made prior to the replacement of an arbitrator under this section is not invalid because there has been a change in the composition of the tribunal.