There is research on gender specific parenting styles. Dr. Brodzinsky distinguished between parenting styles and parenting competency. That the competency increaseses with the amount of time that the parent spends with the child. That a style can be more soothing and nurturing (more often associated with mom) or more playful (more often associated with dad), but that either gender can have these parenting styles and it is not a reflection of competency.
Studies that show single parenting usually is reflective of predictors that can effect child adjustment such as a breakup and loss of the parents or a situation where the other parent has never been involved. Resources are more limited and the single parent is trying to manage everything by him or herself causing stress and less time for the child(ren).
Children who end up doing well with a single parent are because other predictors have helped to compensate: warmth of the parent, mental health of the parent, a parent with sufficient resources.
Dr. Brodzinsky walked through the various research studies and discussed. He pointed out that the studies that compared children who were planned for and brought into the lives of same sex parents (either by adoption or assisted reproduction techology), and subsequently raised by those parents is the most reliable comparison to children born to or adopted by opposite sex couples who remained together while they were raised. Adoption placment at infancy is also distinguihsed from adoption at an older age.