Adoption is a VERY serious issue. You must go through an adoption attorney. not only does the mother have to terminate her rights and consent to the adoption, so does the father. 
You gave us very little information so it appears you are not going through this the correct way. Most states have a procedure that must be followed for adoption and a home study might have to be done and a background check. 
Mom cannot just sign and notarize a piece of paper. She MIGHT be able to give you some sort of guardianship over the child, but it will not be a legal adoption. Also, where is Dad? You cannot just eliminate him out of this. The Father has first rights to the chilld if Mom does not want the baby. 
PLEASE see an attorney. I sense a HUGE disaster here, and I am concerned for the child if this is not done right.