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Child support is always modifiable and so is alimony unless there is a specific agreement between the parties otherwise. Even then a judge can overrule an agreement on child support since that right actually belongs to the child. There has to be a substantial change in circumstances to justify a change. The Uniform Child Custody jurisdiction is a Uniform Act adopted by almost all the states that sets out which state will have jurisdiction over custody issues. As long as one parent remains in the original state, then that state retains jurisdiction unless the parties agree differently.
Then there is the Federal Prevention of Parental Kidnapping Act