Yes, I agree that you must file your petition with each county individually. As to timing, very often the petition will be sent to the original judge, or if not, the presiding judge will review it. Some courts will require a hearing on the petition. In the Los Angeles area, up to 8 weeks is not uncommon, but I would defer to local counsel in the Bay Area. Good Luck.
File in each county.. You must also provide notice to the DA. As long as you do not owe fines/fees and have completed all of your terms of probation, you will likely be granted the expungement. Please keep in mind that you still must disclose the conviction if you are job hunting for "government" jobs or any position that requires a professional license. Also, if these are felonies look into whether they can be reduced to misdemeanors and expunged. Good luck!
You need to have each conviction expunged separately. How long it will take to have the hearing or otherwise get the expungement granted can vary depending on the court the conviction is. I would recommend contacting an attorney in each county to get some more specific answers to your question, and to get assistance in petitioning the courts for the expungements
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One thing to realize: there is no such thing as true expungement in this state! There is the 1203.4 quasi-dismissal that undoes some aspects of a conviction, but unscrupulous attorneys sell their services to "expunge" one's record, and that legally cannot happen in this state for adult convictions. You do have to do the 1203.4s one conviction at a time, county by county, but beware the limitations on the effect of that post-conviction "dismissal." You probably need to hire counsel to perfect this, and hire one that does not label what he/she is doing as "expungement."
There must be a separate petition submitted for each offense, but there is no special requirement that says that one must be expunged before the other. What determines whether they can be expunged is the severity of the crimes, how long ago you were convicted, and whether you're on probation now. I could have the convictions expunged in a matter of a few months. Feel free to give me a call or write me a message if you would like some help with this.