The Facts of Fatherhood

Lacquer suggests that we "abandon the notion that biology--facts--will somehow provide the resolution," and, for the most part, I agree; after all, if biology were never ignored, then perhaps people who had given up their children for adoption would, somewhere down the line, be able to reclaim ownership of that child, despite the lack of any emotional connection. What, then is a parent? Because if we ignore biology, then how can child support be enforced in a case in which a struggling single mother cannot get the "father" or "man who impregnated her" to pay child support? If the notion of biology is abandoned, could this deadbeat get away with not paying child support, since he never acted as or felt like the father?