I have 3 kids and support them solely by myself. Their father has not seen them in 16 months by his choice. We share joint custody, I have been offered a new job in San Diego that will be a great opportunity for us. Can I just up and move? I sent my ex a certified letter to what I think is his last address stating the plan and new address. Is there anything else I should do to cover myself.

I would speak to a lawyer since it sounds like you have a legally binding joint custody agreement. If you have papers that have been certified through a court of law you need to read them. Find out what it says in your papers before you just up and move. If the father does not have a problem with this get the papers modified in court to cover yourself in case he decides to change his mind about it later.

What does the child custody agreement state about you moving out of state? If it does not say anything, you are free to move

In our divorce agreement there is a section that states: The parties should be awarded joint legal custody of the minor children, with primary physical custody in __________________ and periods of care and responsibility consistent with the best interests of the children.

The blank was never filled in... so would that mean I am clear?

Could be, call a lawyer in the state the papers were filed in and get a consultation, usually they are free or very inexpensive. They can tell you if you are in the clear, I would be sure before you go just so nothing can backlash on you later. Oh, and document that you asked a lawyer too, just in case.