Cal. Pen. Code § 1053
If after the commencement of the trial of a criminal action or proceeding in any court the judge or justice presiding at the trial shall die, become ill, or for any other reason be unable to proceed with the trial, any other judge or justice of the court in which the trial is proceeding may proceed with and finish the trial; or if there be no other judge or justice of that court available, then the clerk, sheriff, or marshal shall adjourn the court and notify the Chairman of the Judicial Council of the facts, and shall continue the case from day to day until the time that the chairman shall designate and assign a judge or justice of some other court, and the judge or justice shall arrive, to proceed with and complete the trial, or until such time as by stipulation in writing between the prosecuting attorney and the attorney for the defendant, filed with the court, a judge or justice shall be agreed upon by them, and the judge or justice shall arrive to complete the trial. The judge or justice authorized by this section to proceed with and complete the trial shall have the same power, authority, and jurisdiction as if the trial had been commenced before that judge or justice.
Ca. Pen. Code § 1053