Auxilliary benefits is the word SSA uses for children/spouses/widows.

Your lifetime earnings and quarters of coverage are used in a formula that determines your monthly SSA benefit (Primary Insurance Amount - PIA). The PIA is the amount you get monthly if you have no offset for worker's comp or public disability benefits. In a retirement claim, the PIA is the amount due if the claim is filed at full retirement age. If retirement is at age 62, the monthly amount is less.

The family maximum amount is between 100% and 150% of the PIA. The family maximum determines the amount that can be paid to the entire family. In a claim involving a younger individual who has just enough quarters of coverage to be 'insured for benefits' (worked just barely enough), may end up with a family maximum that equals the PIA. In many disability cases, because the family maximum equals the PIA, the children are technically entitled to benefits, but no money can be paid. If the family maximum is 101% to 150% of the PIA, then that amount is divided among all auxilliaries on the record who have filed claims.

In order to get benefits for children, someone has to file a claim and prove they are your biological children. Naming them on your disability applications may protect their right to retroactive benefits, but that doesn't last forever. Sometimes adopted and step and dependent grandchildren can qualify; additional rules apply. SSA will also have to decide who to name as representative payee. It is generally the adult with custody of the child which is not always the disabled parent. There can be several 1/2 siblings.