If you have recently moved, then you should inform them of this immediately.
A change of custody must be filed through the courts. A change in child support should also be filed through the courts.
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no
That's determined by the courts, and will depend on a number of factors.
Um, why? Is your ex-wife hiding from you?
As the father has no assumed rights to the child, he can still be ordered to pay by the courts.
The courts would have to approve this.
In Alabama, a child cannot choose where to live. The courts will make that choice.
I don't think it's entirely up to the child where they live until maybe about age 17 in Illinois. Placement usually depends on what the courts believe is in the best interest of the child though sometimes they allow input from the child.
Once an order is in place, it does not automatically stop if the child is not longer residing with the obligee parent, nor is that parent required to report the fact to the courts.