California Code, Probate Code - PROB § 2660

A guardian or conservator may at any time file with the court a petition tendering the resignation of the guardian or conservator. Notice of the hearing on the petition shall be given for the period and in the manner provided in Chapter 3 (commencing with Section 1460) of Part 1. The court shall allow such resignation when it appears proper, to take effect at such time as the court shall fix, and may make any order as may be necessary to deal with the guardianship or conservatorship during the period prior to the appointment of a new guardian or conservator and the settlement of the accounts of the resigning guardian or conservator.