Your custody and dependent situation becomes very important here, and is sometimes even more tricky to figure out in the year you divorce. You will want to read publication 501 and 504.
https://www.irs.gov/pub/irs-pdf/p501.pdf
https://www.irs.gov/pub/irs-pdf/p504.pdf
Very briefly, the parent who the children actually lived with more than half the nights of the year is the parent who can automatically claim the child or children as dependents. Most of the time, the child can't live more than half the year with both parents. However, in the year you split, it can be possible for a child to live more than half the nights of the year with both parents. For example, if you separated on March 1, then the children lived 60 nights with both parents. If you then shared custody 50/50 after that, then both parents get "credit" for 210 nights of custody, and both parents have the right to claim the child as a dependent because 210 is more than 183. If you agree, you can split the children any way you like, and neither parent needs a form 8332. If you can't agree, the first tiebreaker is which parent the child lived with more nights (even 1 day difference, like 210 days vs 209 days). If it is exactly the same number of nights, the second tiebreaker is which parent has the higher taxable income.
In future years, this becomes easier to figure out because its generally impossible for each parent to have custody exactly half the nights of the year since there is a odd number of nights; only one parent can have actual physical custody more than half the nights of the year.
