My boyfriend and I have been arguing all the time, last night he took my truck (that is in my name only) and stayed out all night. I don't want him living here any more it is not good for my children (who are not his. This is my house he is not on the mortgage, can I have him move out now or do I have to give him time? In Arizona

The key words here are 'have him move out now.'
Of course you can say move, I don't want you here, get out, maybe even I'll chip in on your first month's rent.
Legally he can refuse and you have to go through the formal process of eviction according to AZ law.
Start with a letter (the kind on paper, maybe given to him with an impartial witness present, and of course keep copies), and then go to city hall and get the paperwork started.
How did he get your car keys? Time to start locking up everything in sight, failing to cook for him, and making life there a little unpleasant but not such that he would hurt you or the kids.

Most likely he has established residency and has to be treated like a month-to-month tenant. That means that you have to give him a written notice that his tenancy is terminated and he must move out within 30 days. If he doesn't move out within that time then you can file a lawsuit for eviction.