Common law marriage is not recognized in California. There is no community property or spousal support for parties that have lived together and were never married.
However, courts will recognize valid non-marital relationship contracts. Contract law applies to any of the property, real or personal, that the parties acquire during the time they lived together. These are referred to as a Marvin action or Marvin claim. Marvin v. Marvin (1976) 18 Cal.3d 660.
Since these cases deal with contract law rather than family law, they should be filed in civil court rather than in family court.
In evaluating any Marvin claim, proof of names on title to property, accounts, wills, trusts, etc. are critical in establishing the claim.
If you have a child with your partner, then the appropriate action is to file a request for child support with the Department of Child Support Services (DCSS) and/or file a Petition for Paternity/Parentage to establish custody and visitation orders.