To adopt an adult in New York, the parent must submit an application to adopt. Upon receiving the application, the state of New York will.
DOH-4455, Adoption Information Registry Birth Parent Registration Form, PDF. LDSS-2725, NYS OCFS Request/Response for Name and/or address of Father.
In the state of New York, a person may choose to adopt someone over the age of 18 in order to grant them the same legal Adoption.