You answer zero months to how many months child lived with you. Follow the rest of the viewpoint and it will allow you to claim the dependent, as the non custodial parent.
The
custodial parent has first priority on claiming the children on her taxes;
regardless of the amount of support provided by the non-custodial parent. The
non-custodial parent can only claim the child as a dependent if the custodial
parent gives permission (on form 8332) or if it's spelled out in a pre 2009
divorce decree. Even if a divorce decree, dated after 2008,
gives the non-custodial parent the right to claim the child, he must still get
form 8332 from the custodial parent. A properly worded decree should require
her to provide that form. https://www.irs.gov/pub/irs-pdf/f8332.pdf
Furthermore, there is a
special rule in the case of divorced & separated (including never married) parents.
When the non-custodial parent is claiming the child as a
dependent/exemption/child tax credit; the custodial parent is still allowed to
claim the same child for Earned Income Credit, Head of Household filing status,
and day care credit. This "splitting of the child" is not available
to parents who lived together at any time during the last 6 months of the year;
then only one of you can claim the child for any tax reasons. The tax benefits
may not be split in any other manner.
Note in particular
that the non-custodial parent can never claim the Earned Income Credit, Head of
Household filing status or the day care credit, based on that child, even when the custodial parent has released
the exemption to him.
