If my dad and I are joint owners of the house, who gets it when he passes away?

Question Details: My father and I are co-borrowers on the mortgage and we are both on the title of the. My mother had bad credit so that is why I am on it instead of her. I also have a half-brother from my father's previous marriage. My father does not have a Will. What happens to the home when my father passes away? Can my half-brother be able to come after the home and get his part of the equity or try to buy me out of it or is he not entitled to anything? I want to ensure that my mother and I are safe. My half brother had no interest in being a part of this family so I do not want him to come around trying to get money out of our father's death. I live in CA.

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