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The parent claiming the exemption is the parent with whom the child lived more than 1/2 of the year, including temporary absences due to education.

I should note that my ex has never provided a roof over our son's head.  

That sounds like he's not parent that the child lived with more than 1/2 of the year.

Now that my child is over the age of 18, my ex is demanding that he gets to deduct our son on his taxes and has threatened to take me to court if I don't agree.

In a dispute with the IRS he will lose.  However, if he is still paying child support it's difficult to predict what a Family Court would order.