Step parents legal rights over a child that is not theirs biologically depends on the legal proceeding and the biological parents involvement. In general, step parents have no legal rights over a non-biological child unless they have legal custody.
General Step Parents Rights
Because a step parent is not biologically related to a child, she has no rights in regards to that child's placement, health or welfare. This does not mean that the step parent does not have an obligation to ensure that the child is well cared for, but rather that the step parent has no right to dictate who has access to the child. This means that the step parent cannot control another parent's involvement with the child.
Similarly, a step parent cannot petition the court for custody over the child during a divorce proceeding. Custody of a child will always be given to a blood relative over an unrelated individual.
A step parent cannot dictate a non-biological child's medical care, education or other aspects of his life. This means that a hospital, school or other institution cannot provide or deny services to a child based on the step parent's rulings. This is not the case if the step parent adopts or has been granted custody of the child.
Step parents may influence a court's decision about the child's custody if they provide the court with evidence of why a parent should not have access to the child. An example of this is if the step parent knows that the non-custodial parent abuses the child. Also, if a step parent is the only remaining parent to the child and the step parent and the child have a good relationship, the court might grant a step parent custody.