You may adopt your adult step-daughter and this is in fact donw quite often as a means of solidifying relationships for purposes of probate. Its a defense to will contests.
An adult adoption is when someone adopts a person who is over 18 and not related to them. The person adopting must be at least 10 years older than the adult they are adopting.
You must file these documents with the Court:
Type them on pleading paper. You can get pleading paper at bookstores or stationery stores. There are no Judicial Council forms for adult adoption.
The Petitioners (this means the adoptive parent and the adoptee) must file a Petition. This is the document that asks the Court to make an Order approving the adoption. It must say:
-The name, age, date and place of birth of the Petitioners
-How long the Petitioners have known each other
-Why the Petitioners want the adoption to take place
-If either Petitioner is married, the name of the spouse (if any), the date of their marriage, and the names and ages of their children. If spouses have signed consents to the adoption, list their names and dates they signed the consents. Attach the consents to the Petition.
-The date your adoption agreement was signed. (Attach a copy of the adoption agreement.)
-Whether the adoption is in the public interest
Special note: An adult adoption changes the legal rights of the adoptive parent and adoptee. Adult adoptions are very complicated. Your petition must contain specific words. Talk to a lawyer first.
This is the agreement between the person to be adopted and the adoptive parent. Both must sign and date the Agreement. The Agreement must say you both agree to assume the legal relationship of parent and child and all the duties and responsibilities of that relationship.
You must also agree to file a petition in the Superior Court of California. Your Petition must ask the Court to approve your Agreement and to make an adoption Order. You do not have to notarize the Agreement.
I would talk to an attorney before I did all of this. He or she will want to review the facts, and can help streamline this process.