how long does a new car dealer have to release the paper work in order for you tag your new car, after the car was paid in full and the check cleared

Generally speaking, the dealer must transfer title to you on your demand after you have paid for the car. Practically, the dealer is entitled to a "reasonable" time to determine that your check will not be returned unpaid and to process the papers. That might be a few days to a week, or possibly longer.