Tenant at Sufferace
The presumption is that you are a tenant at sufferance. A tenant at sufferance has few rights, but one of these rights is to be evicted. So in other words, one cannot simply physically kick you out of the home. You must be evicted like a tenant who has not paid rent and first given 60 days to leave. If 60 days passes and you do not, he can pursue eviction. This is true even if you have lived together for some time.
There is no common law marriage in CA. However, there is PALIMONY. See HERE. This is essentially an application for support after a break up of long term partners, even if not formally married. In addition, one can request child support for the child. So while he has right to ask you to leave, someone in your situation can use the threat of filing for palimony/child support as leverage to ask that he not demand this, or buy you some time, etc... or actually simply FILE for it anyhow.
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