In the UK there is a concept of "child of the family" - based on whether the child, legitimate, illegitimate, of different parentage, fostered, adopted, whatever was "treated as child of the family". In such a case a person may have parental responsibility, irrespective of DNA - I oversimplify of course. That seems to me to be morally right, insofar as addressing the responsibility of the adult to the child. Basing all on DNA seems to me to be very primitive.

But as between the adults it is different.