Survivor benefits for dependent children

Please note that determining paternity alone may not lead to benefits. This is not a simple issue, but consider this ruling for reference :
http://www.ssa.gov/OP_Home/rulings/oasi/09/SSR89-09-oasi-09.html

The general criteria for entitlement to child's insurance benefits are
found under 42 U.S.C. § 402(d)(1). Section 402(d)(1) provides that every
"child" of an individual who dies fully or currently insured under the Act
is entitled to child's insurance benefits if the child has applied for
such benefits, is unmarried, under the age of 18, and was dependent upon
the insured individual at the time of the insured's dead. Id.

A child is deemed dependent if he was (1) living with or supported
by the wage earner at the time of his death, or (2) is the legitimate
child of the wage earner. 42 U.S.C. § 402(d)(3). If a child is

illegitimate, he may nonetheless be deemed legitimate for
purposes o the Act (and hence deemed dependent and thus entitled to
benefits) if he can [establish]: