The legalities

From Adoption.Com:

Adoption bestows on the adoptive parent(s) all the rights and responsibilities of a legal parent, and gives the child being adopted all the social, emotional, and legal rights and responsibilities of a family member. Sometimes, court language will include the words "as if born to" to describe the new parent-child relationship.

Before parental rights are assumed by adoptive parents, the court determines that biological parents have, legally and with full understanding, either voluntarily relinquished their parental rights, or that those rights have been terminated by the court. Depending on the circumstances and state laws, these two actions - the severing of biological parents' rights and the bestowing of parental rights on the adoptive parents - may be done at the same time, at finalization.

During the court finalization hearing, the judge reviews information about the child, the biological parent(s), and the adopting parent(s). This information can include:
the homestudy and/or other evaluation of the adopting parent(s) and their suitability for the child, reports of pre-adoption counseling and education for both placing and adopting parents, case workers' notes and recommendations, and other reports.

Those who appear at the finalization hearing (either separately or together), in addition to the Judge, may include, but are not limited to:
Adopting parent(s)
Their attorney
Placing parent(s)
Their attorney
The child/ren
The child's legal advocate and/or caseworker
Adoptive parents' caseworker
Placing parents' caseworker

The Judge reviews all supporting information about the adopting and placing families, and may ask questions of all parties, including the child/ren if they are able to communicate their feelings and wishes. The Judge will then approve or disapprove the petition to adopt.

If approved, the adoption is finalized and an Adoption Decree is issued.

In most U.S. jurisdictions, at the time the adoption is finalized, the child's name is legally changed, and the court orders the issuance of a new, amended birth certificate for the adopted child. This amended birth certificate replaces the name(s) of the biological parent(s) with the names of the adoptive parent(s), and replaces the child's birth name with his/her new name.

The original birth certificate and other documents relating to the adoption are sealed, and are generally not available to parties to the adoption, as detailed in state law in the U.S.”

Credits: Sandra Hanks Benoiton