"Stepparent adoption" refers to the legal process where a stepparent assumes legal rights and responsibilities for their spouse's child, as if they were their own, through an official adoption. Full definition
The only exception is in stepparent adoption of the child. (divorcesource.com)
This requirement is often waived for stepparent adoptions because the child is already in the legal custody of one biological parent but check with the court to be sure. (thespruce.com)
In California, married couples or registered domestic partners are allowed to adopt the child of their partner through stepparent adoption procedures, as opposed to the more complicated independent adoption process. (marriage.com)