STATISTICALLY SPEAKING, there is no question that children in intact, Mom&Pop households have better life outcomes than people in single-parent or abusive households. There is simply not enough data yet on the outcomes from "gay" households, despite what many pro-gay organizations want you to believe.
STATISTICALLY SPEAKING, people who (1) graduate from HS, (2) defer children until they are in a stable marriage, and (3) get a job - any job, reduce their chances of living in long term poverty by 80%, when compared to people who ignore those three mandates.
If a single woman has the resources to nurture a child: financially, emotionally, child care alternatives, and so forth, she might be successful, but STATISTICALLY SPEAKING - looking at thousands of similar cases nationwide, and comparing them with kids raised in intact Mom&Pop households, the child would be better off with a father.
In my own white, middle-class family, there are four "illegitimate" children who have been born in the past dozen years or so. In all cases, the mother had the complete support of HER family - financial, babysitting, housing as necessary, healthcare expenses, schooling (parochial school tuition), and so on, and the kids are doing fine. But without that family safety net, they would not be doing "fine" at all. Indeed, if the mothers were on welfare (etc), it would be a bad situation indeed. And the mothers have been able, with that family support, to continue in their professional lives as well as they would have with a husband. (One bi-racial child in this group).