If the mother is unwed with a child, and no child support or court order is in place, what are the restrictions on the mother to travel or take residency in another state?

If the mother is unwed with a child, and no child support or court order is in place, what are the restrictions on the mother to travel or take residency in another state?

No restrictions.

And she can take the child with her.

For that matter, the father can do the same thing.