Illegal Alien is Father, Does He Have Rights

My question involves a child custody case from the State of: Nevada

Does my ex(never husband) have any legal rights to take our American born kids into his country of Mexico?

I have a job that pays all our bills and plenty of blood relatives around me that support is not an issue of any kind.

Has paternity been legally established?

Are there any orders in place?

No blood test had been done, but I am 100% sure it is his.

He claims to have talked to lawyers, and at this point only made threats. How much do those type of lawyers cost? Is it cheap enough for me to talk to a lawyer?

I receive money from him some of the time, he is by no means consistent about it, but I do want him to keep it regular. My biggest fear is that they will be at his place one day, and then he will vanish into Mexico. Even if it is considered kidnapping i don't think the stats on that sort of thing are very good for retrieval.

If paternity hasn't been legally established you are under no obligation to allow any visitation - period.

He would also need your written permission to remove the kids from out of the country.

Wait, I am confused as to how legal paternity is established? If he is on insurance or if the hospital has him listed as the father. How do I find out if he has legal paternity?

What does your court order say?

What do the kids birth certificates say for "father"?

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Quoting PQN

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What does your court order say?

What do the kids birth certificates say for "father"?

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The birth certificates have him listed. What steps do I need to go through in order to keep my kids? He keeps threatening.

What steps should I go through in order to keep my kids, especially to keep him from moving?

You can't stop HIM from moving.

You're not married to Dad, correct? Until he goes to court to establish custody/visitation, you are not legally obliged to allow any contact at all.

I'm not entirely sure what you're hoping to attain here though.

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Quoting Dogmatique

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You can't stop HIM from moving.

You're not married to Dad, correct? Until he goes to court to establish custody/visitation, you are not legally obliged to allow any contact at all.

I'm not entirely sure what you're hoping to attain here though.

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Only two goals is to keep him from moving to Mexico with the kids. Or him taking the kids away from me. Just making sure my bases are covered before hand. This is something he has threatened to do, so I don't know if he can do these things, or how he would go about doing it legally.

In terms of actually moving with the kids, he could do it one of two ways...legally or illegally.

Legally, he would need to obtain custody of the kids and permission from the court to relocate the children (assuming you don't agree).

Illegally - well, if he's going to take the kids and run he's going to do it anyway. Then you'd have to go to court to get an emergency order for the kids to be returned; and even with such an order, as a practical reality it's not always easy (and in some cases not always possible) to get the children back to the US.