This question is a little unclear. I've read it three times, and came up with three different ways that the facts could go. It sounds like, at its core, that you are the master-tenant living on a month to month lease and have an ex-partner who used to pay rent to you but now no longer does.
The basic question, however, is whether there is such a thing a squatter rights. The basic answer, in a landlord-tenant situation is no. Either you are a tenant, a tenant who is holding over, a licensee/invitee, or a trespasser. A true squatter is basically a trespasser on someone else's land. If that's the case, there are virtually no rights to possession. If one is a tenant, then they have the right to possession subject to the terms of the lease. If they are a tenant holding over, then they came into possession legally but are now holding the possession without the permission of the landlord.. (This is all very simplified for the purposes of this answer.)
So what are the options? Based on the information you've given (that you have some sort of either master-tenant relationship with the ex-partner or are the property owner) then you have to proceed through the unlawful detainer procedure. The one right that a "squatter"/tenant holding over has, is to not be kicked out of the property by a landlord's self-help. This includes calling the police and saying that the person is a trespasser. In order to start the procedure, you will need to give them a written demand which complies with the Code of Civil Procedure.
However, since it sounds like this is a roommate situation, you might want to try talking to the person first and seeing if you can arrange some sort of amicable departure for your ex-partner. Living with someone whom you are trying to evict is, from what former clients tell me, not pleasant.
If, on the other hand, you cannot work something out, it would be worth your time to consult an attorney who practices Landlord-tenant law. While unlawful detainer proceedings are "summary", they can be tricky and if they are not done properly, can result in significant problems. You're best bet would be to start off with your county's local bar association. Most, in California, have, referral services that can help you find an attorney.
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