Want to move out of Texas with my children have not been served any papers can I move

Welcome to AMHD. I would think so. Are you speaking of a divorce case? Our law generally does not favor 'prior restraint', such as an order restraining you from moving with your children. But there are domestic relation laws to prohibit a parent from escaping the jurisdiction for one reason or another (don't know what your reason may be). Texas courts may retain jurisdiction of your case, anyway, so your reason for leaving should be legitimate. If you have not received notice of such a restraining order, then you are probably free to leave.

Sure, but if your ex files before you establish residency elsewhere you may be required to move the kids back.