Aren't you afraid their birthparents will come back and take them?

Sometimes I do find myself peering around corners at the park or eye-balling strangers at the museum.  This is a substantial difference between domestic and intercountry adoption that you should explore in your heart before you choose an adoption program.  Legally, our children are ours, and that cannot be revoked, despite what the latest Lifetime movie says.  What I fear most is that my domestically adopted son will grow up and search for his birth family.  That in itself doesn't scare me, but the idea that he may eventually choose them over us, leave us forever for them, go to their house for Christmas, bring the grandkids to their place and not ours, etc... does keep me up some nights.  The same possibility is there for our internationally adopted children as well, but for whatever reason it doesn't seem as looming.  It's selfish to want to be their #1 and only mom.  I realize this, but I'm trying to be honest here.