Generally, TP w/ >50% custody (or where dependent spends more the 183 nights per year) is considered custodial parent. and can claim child as dependent, etc. 

However. there can be a clause in a divorce decree or agreement if something else has been agreed to....   i.e.  claim kid every other year... 

There are plenty of other rules that govern the specifics of the situation. See pub 501 https://www.irs.gov/publications/p501