Private adoption agencies have very different policies depending on the private adoption agency. It is not uncommon for adoptive parents in one state to work with a private adoption agency in another state to find a birth mother to match with. There is much flexibility on how adoption can be arranged with private adoption agencies.
All private adoption agencies will work with the birth parents in relinquishing the child and their parental rights to the agency, then the agency will place the child in the family chosen by the birth parents in most circumstances. Different than an independent adoption where the birth mother or birth parents place the child directly with the chosen adoptive family. An adoption attorney may or may not be involved in the adoption process with the private adoption agency, depending on the state laws. Many private adoption agencies do place the children directly from the hospital and to the adoptive parents care depending on the state laws.