At least where I live (and I imagine many other places), the law of parenthood isn't based on genetics. Where I live, the birth mother is legally the mother, and if she says X is the father, and he agrees with her statement–by both of them signing the birth registration paperwork–then X is legally the father. (In most cases; in some cases, if the birth mother is in a marriage or cohabiting relationship with a man, her male partner is legally the father even if the birth certificate names another man, and even if that other man is genetically the father – as in the case I mention below.)
Generally speaking, genetics only comes into the picture if someone launches a court case to dispute parentage – e.g. if the mother says X is the father but he refuses to accept that status. But, if a man signs the birth papers for the child, he is legally the father, even if it isn't genetically his offspring. And likewise, if the mother gives birth to the child, she is legally the mother even if the egg came from someone else.
Genetic parenthood by itself doesn't automatically make you a legal parent. At best, it creates the possibility for you to claim parenthood (if you want to), or for someone else to impose it on you (if they want to).
An interesting court case - http://www.austlii.edu.au/au/cases/cth/FamCA/2009/691.html - found that the birth mother's cohabiting partner was legally the father, even though the genetic father was listed on the birth certificate. This wasn't what any of the people involved wanted – the birth mother was acting as surrogate for her daughter and son-in-law, who were the genetic parents – but was an undesired to all parties side effect of the lack of legal recognition of surrogacy at the time in that part of Australia. The remedy was the genetic parents had to legally adopt the child, even though they had been raising him as their child from the time of birth.