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From http://www.ssa.gov/pubs/10085.html :
Who can get child's benefits
Your child can get benefits if he or she is your biological child, adopted child or dependent stepchild. (In some cases, your child also could be eligible for benefits on his or her grandparents’ earnings.)
To get benefits, a child must have:
The child also must be:
The child may qualify under the parent's disability.