Legal Question in Family Law in California

Not unless you adopt the children.

Actually Sher's answer is not QUITE entirely true. Under some VERY unusual circumstances a step-father can become responsible for his step-children even without an adoption. There are a lot of details that would go into determining if that were the case, but the short version is that if he acts in all respects as if he had adopted them, including the real father not being in their lives and the step-father holding them out as his children, the law might ignore the fact that he did not go through the formalities. Most often, however, this only comes into play where either the step-father seeks reimbursement for supporting the step-kids, and the court says "no, you treated them as your own so don't now come ask for the money back," or where the kids would go on public assistance and the court finds that the step-dad can't dump kids on "the system" after treating them as his own for years.

If you received the children into your home, and held them out to be your children, arguable you are the father by a doctrine known as parentage by estoppel.