If you were previously settled, had job, lease, etc. and stayed for over a certain amount of time (depends on the province) yes you can move. In the case of Alberta to Ontario, Alberta would continue to pay your healthcare costs for 3 months before OHIP kicks in. No you can't just move to give birth or you will be asked to repay the cost of delivery. You will have to commit to settling in Alberta. In general trying to play the system it is a bad idea because it will likely cost more than paying for a delivery.
