How NOT to run a welfare system...

New Zealand seems to be providing an example of that:

Even with a huge shakeup of social welfare announced last week, strict rules around government support for teenage parents means Liam and his partner Sheridan are better off financially if they live apart and raise their young son separately. If they lived together as a family Sheridan would not be eligible for the Domestic Purposes Benefit.

And why wouldn't they? It worked so "well" in the US after all:

... that’s exactly what the United States did with its welfare system back in the 1960s and 70s. In order to qualify for Aid to Families with Dependent Children, a mother couldn’t have a man in the house with her and the kids. In other words, the government paid the mother to keep the dad away. That explicitly encouraged the marginalization of poor fathers in the lives of their children. Many still regard the AFDC rules as greatly responsible for the wholesale breakdown of African-American families that still plagues us today.