In Victor Hugo's novel, Jean Valjean tells a dying mother that he will care for her daughter, Cosette. The mother gives him a letter authorizing him to care for Cosette. He goes to the inn where the daughter is being cared for, and pays off her expenses. They disappear into a convent for about eight years, and then begin living openly in Paris. He always treated Cosette well, and they had plenty of money.
I'm curious: if such a sequence of events were to play out in the present day (in the United States, let's say), how would the legal system react? (I'm not sure exactly how anyone would know; presumably some situation would arise when a birth certificate would be needed.) Is there some concept of “common law adoption,” or would the courts start from scratch in determining who should take care of Cosette? Would Valjean be guilty of a crime?