Jackie, a "private adoption" is not the same thing as being placed by a private agency.
A private adoption does not use an adoption agency for the placement. The adoptive parents might be selected by an attorney or a physician. If the birth mother selects the adoptive parents, it's an open adoption.
In a private adoption (also called independent adoption or gray market adoption), the judge may assign the task of a routine investigation to an agency, however, at the time the adoptive parents go to court seeking legal sanction for the placement. This agency could be the state welfare department.
Now, what is a "private agency"? It is one that is not a government body (such as a branch of the state welfare department or a county social services department). It would be a company---either nonprofit or profit-seeking---that is licensed by the state department of welfare to place children for adoption.
Reg Niles
RegNMINiles@cs.com