Can both parents sign custody over to a woman who is not related to the child?

Probably - see CA Family Law Code

3040. (a) Custody should be granted in the following order ofpreference according to the best interest of the child (1) To both parents jointly the court shall consider, among otherfactors, which parent is more likely to allow the child frequent andcontinuing contact with the noncustodial parent, (2) If to neither parent, to the person or persons in whose homethe child has been living in a wholesome and stable environment. (3) To any other person or persons deemed by the court to besuitable and able to provide adequate and proper care and guidancefor the child. (b) choose a parenting plan that is in the bestinterest of the child.

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