That's less and less of a concern: firstly, there are far far fewer adoptions this century due to both acceptance of being a single parent and because of access to abortion and birth control. Secondly, it won't be long before every adopted child learns about DNS testing in school and as soon as they are of age (or can fake ID) they will find relatives [Source: have volunteered in the field].

This will lead very quickly to no more anonymous adoptions. I'm in favour of open adoption as studies have shown it's healthier for the child but that's my own personal bias outside of the technology.

Edit : DNA testing...