The parent who lived with the child for more days than the other parent will be eligible to claim the child as long as that parent is not also claimed as a dependent on another tax return.
The child must not have provided more than 50% of their own total support.
The father must have a signed Form 8332 (or it's equivalent like divorce decree or other court document) from you giving him that right.
If the father and you lived with the child equal number of days during the tax year, the parent with the highest Adjusted Gross Income is entitled to claim the dependent.
http://www.irs.gov/pub/irs-pdf/p501.pdf This link will take you to the test for tie breaker rules to be used when more than 1 person wants to claim a dependent.
Support provided by a combination of BOTH parents is used to satisfy the support test . It does not matter which parent actually provided the funds.