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Your child can get benefits if they’re your biological child, adopted child, or dependent stepchild. (Sometimes, your child could also be eligible for benefits on their grandparents’ earnings.)To get benefits, a child must have:• A parent who’s disabled or retired and entitled to Social Security benefits; or• A parent who died after having worked long enough in a job where they paid Social Security taxes.The child must also be:• Unmarried;• Younger than age 18;• 18-19 years old and a full-time student (no higher than grade 12); or• 18 or older and disabled. (The disability must have started before age 22.)
Within a family, a child can receive up to half of the parent’s full retirement or disability benefit.
The family maximum payment is determined as part of every Social Security benefit computation. It can be from 150 to 180 percent of the parent’s full benefit amount.
The money belongs to the child.
There is no specific requirements to save the money or to use for any specific purposes (like for education).
The check is issued with the child's name OR
if the child is a minor - with the name of the custodial parent who manages the money on behalf of the child.
See here - that is teh determination used by the SSA - it is possible that both parents are Custodial parents.
6. Custodial parent
A custodial parent is a parent who has care, guardianship, or custody of the child.