I guess to be clear does a father have 50/50 rights the same as the mother or does she have legal custody at birth.
The former in most places. Both parents share full custody (Not 50/50, which seems to imply a right to 50% of the time. Both parents share the right to 100% of the time, actually.). There are exceptions to this in some states. I discovered a few weeks ago that, in Illinois and another mid-western state I think, that there is a presumption that in effect gives an unwed mother primary custodial rights.)
You should check your state statutes (usually in the title relating to parent/child, marriages, or something like that) to be sure.