it all depend's on what state you are in because every state has there own law's.

Now for custody battle's it's not a easy as you think to gain sole custody of a child first you have to proof that the other is unfit to raise a child not only that but also if the other parent has not seen his or her own child for some time it's what you may call Abandonment that also can be use as testamony but it all depend's on what ground's your seeking.

And ofcourse there's also abuse if the other parent either negleted or abuse the child in some way that will give you sole custody so there's many differnt ground's that can be used but also it can cost a large sum of money and laywer fee's .