I think the effect can be in two ways. It's either positive or negative. I like to use my experiences to judge and from what I've observed, it's most times negative than positive.
You see, the father figure usually imposes a sense of discipline on the child and helps form a sort of a model for appropriate behaviour. You have mothers who constantly prevent their children from doing evil by threatening to report to their father. The father of serves as the logical part of the equation a the mother is the emotional.
In homes where the father is lacking, the tendency does the child to become wayward and exhibit violent behavior becomes higher than can be said for the home whereas both parents are present.
I recall a home when I was growing up where the father died in an accident. After all the burial and rites had been done, I began to notice certain behavioural modifications in the children. First, the guys didn't keep late nights before and would like return home before 8pm. When the dad died, it was not uncommon to hear them banging on the door by 10 or 11 pm. I knew cause we lived in the same building,though different apartments. This is one of the negative aspects of the absence of the father figure.
Also, if the father of figure is around, there would be less emotional attachment to them mother. The child would know that there is competition for attention from the father and would have to caution himself or herself as to the closeness to the mother. While peers and friends could severe that emotional tie to an extent, a child who grows up not having a dad would barely be able to withdraw from its mother.
The good side is that there may be a drive towards excellence on the part of the child to ensure that the mother is proud of her child. The child may want to do well and behave properly so he would not cause the mother more pains. It won't be uncommon to see such a child excelling in book work and being of good behavior.
So, the results are in two ways.