Yes.
A birth father is a genetic father of a child, as opposed to an adoptive father or stepfather.
An adoptive father is a man who has adopted a child.
A mother in law.Stepmother. Adoptive mother Foster mother female parent to be the mother of A woman who gives birth to a child
Only the biological father can sign his name, if that is what you mean. If the child is adopted the adoptive father can change it and sign his. If the mother sign his name or another man's name, it is fraud. The mother must always be listed on the birth certificate.
That varies widely depending on the jurisdiction and the circumstances of each case. Usually, the adoptive parents bear this cost.
The word adoptive is an adjective meaning "one who has adopted." An adoptive mother would be one who has adopted a child who was not born from her. At the time of the adoption, the child becomes legally hers, just as if it were born from her.
In the United States the rights of a birth mother to contact an adopted child are determined by state law. If an adoption agency handled the adoption, then the birth mother has no rights until the child is of legal age. After that, the adoption agency will usually help the birth mother find the adopted child.
Here in the Philippines, a mother can not just name any person as the father of her child in the Birth Certificate. They will look for a marriage contract as their reference when you named your child under his/her father's surname. Or if not married, they let the father fill up the Affidavit of Acknowledgement/Admission of Paternity at the back of the Birth Certificate.
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She can; that would be a private adoption and would still require either an agency or a lawyer, since the father-to-be would have to undergo the same home study process as any adoptive parent.
Who legally adopted the child?If the mother's new husband legally adopted the child, then the biological father's parental rights had to be terminated first. Which means that the biological father is NOT obligated to pay child support anymore. The new adoptive father has taken on all rights and responsibilities for the child.
It could be if they didn't have permission from the adoptive parent.