According to Hebrew and Roman law the offspring of incest or adultery could not be legitimated. Loss of status (capitis diminutio, media or maxima), involved loss of liberty or citizenship, and destroyed the paternal power. Emancipation and adoption had a similar effect. Adoption, which tries to emulate nature, was a means of acquiring the (proper) paternal power.
Our current adoption laws maintain capitis diminutio minima, which involves loss of (original, non-legitimized) family relations in order to acquire the desired status or power of the legally replaced relationship.
I have always loved reading the fascinating stories of twins separated at birth because of the amazingly similarities in things we would never suspect as being genetic, such as career choices. Of course, now knowing that some of these studies were done by involuntary means is extremely disturbing to say the least...reminiscent of Nazi Germany....and done knowingly by a NYC Jewish adoption agency: Louise Wise, makes it all the more repugnant.
That aside - our DNA runs through our children and forms a great deal of who they are, despite nurture and despite laws that make them capitis diminutio minima.