They have to go through some legal adoption procedure. Caring for children or saying “he’s mine” is not ownership.
That wasn't the case with Lisa Miller and her dyke 'lover' Jenkins, though. They only entered a "domestic partnership" in Vermont, and yet, the child that Lisa birthed with an anonymous donor was deemed Jenkins' child also by proximity. So much so that Jenkins successfully claimed the right to visitation, and then sole custody.
Look up the CASE LAW and you will find you are WRONG, if you “HOLD” that a child is yours, even though not biologically related or by any other means, the COURTS in any and ALL CUSTODY CASES will make it so and you will PAY FOR SUPPORT.
I found this out during my own custody hearing 20 years ago when the court granted me Custody of my ex’s Son, as well as my daughter.