Getting "sole custody" as you say is not the easiest of tasks. You can definitely attempt to file a modification action based on what is going, but it also does not sound like he is actually serving time in prison right now. Obviously, if he is in prison, you have sole custody for all intents and purposes. I would not recommend filing anything without an attorney on your side.
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You could probably file for sole custody based on his abandonment of his daughter, but, if he shows up for court (which I'm sure he won't do given that he appears to have a warrant out) or if he files pleadings, you might lose. If you goes to prison, you will almost certainly win, at least for the time he in incarcerated. Why would you want to file, though? Why go to the time and expense? Don't you already pretty much have sole custody, even though not legally? Are you afraid he'll show up and take her? That doesn't seem likely, given the circumstances.
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While the father is incarcerated, you have sole custody since he obviously
cannot exercise any contact from jail.
No one else can use his contact rights unless they file some kind of
pleading and can convince a court to do so, and that is unlikely.
If he is a fugitive, you should not allow contact since he would have to
surrender to the court in order to complain about it.
These are general rules and you should have a lawyer review the facts with
you to be sure they apply.
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