I have had to deal with this question before - which state has jurisdiction if the child truly spends equal amounts of time with each parent, not just when looking at the past history, and in an ongoing pattern?
If the child lived in one state for the six months before the parents separated, and that separation was less than six months before the court case was filed, that state is the "home state" and would have jurisdiction.
But if there is no "home state" fitting the above description, the next thing the courts look at is whether the child has "significant connections" with the state. If there are about equal connections with both states, then the state where the case was filed first is probably going to keep the case.
By the way, when you talk about the merits of who should have custody, you talk about economic things a lot. If you're trying to win or break even in a custody case, those are not what you should emphasize. Yes, it is important not to have economically abandoned your child. But earning more money or being generally financially better off is generally not something the courts will use as a reason to favor you in a custody case.
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