An issue in adoption is that the adopted child and the adoptive parent of the opposite gender will cause yichud (shall we translate that as seclusion?) problems. I just want to quote the Meiri (81b s.v. Kevar): "...However, whomever does this without the intent of yichud and for unclean thoughts, rather, the way of the love of (parents?) the ones who raise a child (derech hamolidim) to publicise and make known that their children are very dear to them, it is permitted. And on this it is said: hakol lesheim shamayim."
With this Meiri, there is no problem of yichud between adopted child and parent. Mipi rabbeinu zt"l.