You should file form 8332 for each of your children. You need to print the forms out and sign each one individually. Enter the years that you are going to allow your children's father to claim the kids in part 2 (part one is just for this year) and then make certain that you sign and date each form.
Then have your kids dad file the return for this year by mailing in his taxes with those forms included. If you have given permission to him to claim the kids in future years in part 2 then he can file electronically in future years. If you are going to fill out a form every year for him then he will always need to mail in the return with forms included.
That doesn't guarantee he won't be audited but it would certainly lower his risk.
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