What are the 49 states unmarried mothers have sole custody?

There is no such provision for 49 states. In some states, a mother is presumed to have sole custody if no father is named on the birth certificate, in other states, a mother is presumed to have initial custody under the same circumstances, other states presume joint custody even if no father is named (someone had to do it, right?) and some states have no presumption of custody at all. For the law in each state, you will have to do your own homework on that.