Needs insight to custody laws

Here's the scenario:

The Mother is served custody paperwork for child by the Father. The Mother decides not to fight it, and shows up to the court hearing to receive visitation rights. The Father did not show and for all Mother & Friends know, the Father left the state with the child. She has been told that by the Father doing that, he has voided his request for custody and that custody fell to the Mother.

:confused:
Q: Does father still have the right to custody?
Q: Who does custody fall to?
Q: Even though the Father did not show to first hearing and for all the Mother knows there have been no other hearings, but could the father have still filed for another one and receive custody without the Mother receiving the paperwork?

The father's rights are governed by the most recent custody order, which apparently gives custody to mom. It's not likely that dad was able to surreptitiously undo the effects of his non-appearance, but if mom wants to check anything he did after the court's custody order was entered will be reflected in the court file.