In Georgia, there is a statutory procedure set out for adoption by a relative of the child. If you have LEGAL custody (such as a guardianship relationship) - more than just PHYSICAL custody - then the easist way to follow through with the adoption would be to have the parents execute a Voluntary Surrender of Parental Rights to you for purposes of adoption - in other words, cover all of your bases. In Georgia, and probably similarly in Ohio, this form is actually set out by statute.
Then, you will be able to follow the steps laid out (again, statutory procedure) to do this. Just make sure that you don't skip over anything, because thoroughness counts in adoption work!