If a father leaves his daughter with a woman, who he believes is his S.O. but she told him she's not, then leaves the state to drive truck for a living... and hardly sends any money for support of the child... would this be considered child abandonment? What can the woman do as the child is 15 (was left when she was 14) and has been in the custody of the other woman for almost a year now?

S.O. means, perhaps, "significant other"?

She could sue him for child support, I suppose.

No its not abandonment. Abandonment is a criminal charge for leaving a child without adult supervision.

So what is it you want? Do you want custody? Support, what?

What "other woman"?