Adoption is a topic that has long interested me and a while back I did some posts on adoption in Babylonia. The person who is adopted had certain responsibilities; but the adopting parents had responsibilities as well.
For instance, if the new father does not teach the adopted child a craft, the child could be returned to the household of his biological father (Hammurabi Law Code, Laws 188 - 189).
Additionally, if a child was adopted by a palace official or the family of a priestess, the child could not be reclaimed by the biological parents (Hammurabi #187). Is this because the child would be better off with the new parents?
Also, the original parents could re-claim the child, but only if they did so very shortly after the adoption took place (Hammurabi #186).
Overall, the Babylonians seemed to make a serious attempt to be fair to everyone involved. The adopted child could not renounce their new parents, but their new family had to provide them with the training needed to make a living.