Legal Question in Family Law in California

No common law marriage in California. The closest we come is the Marvin v. Marvin case that actually applies in very few situations. If the house was bought all cash it would be yours alone even if you married. Never having married, she may have claims on you, but not to the house unless she put money into it.

I assume that your use of the term "with someone," means you cohabitated with someone without being lawfully married.

California doesn't recognize common law marriages, unless the common law marriage was legally entered into in another state that recognizes common law marriage.

California does recognize Marvin actions, which is not the same as common law marriage. A Marvin action is a lawsuit between unmarried parties who had a contractual agreement on how to handle earnings, wealth accumulation and property that was acquired during the relationship.