http://www.nolo.com/article.cfm/ObjectID/F5556B55-E563-42FC-AF277A1A14948708/catID/50577D19-965B-4301-B98AE541654F9EAB/118/246/169/ART/
"Special Rule for Parents Living Apart
If the parents lived apart at all times during the last six months of the calendar year, or if they have a written divorce decree, maintenance agreement, or separation agreement, there is a special rule that applies.
In this case, if the child received more than half of his or her total support for the year from one or both parents and was in the custody of one or both parents during the year, the IRS rules assume that the custodial parent (defined as the parent who has custody of the child for the greater part of the year) should get the exemption for the dependent. However, the parties may change this presumption and allocate the exemption to the noncustodial parent if either of the following are true:"
If parents want to deviate from the CP getting the tax credit they can but in most cases it is clear that the IRS rules assume the CP gets the tax credit because they have the child more than the other parent.
"Special Rule for Parents Living Apart
If the parents lived apart at all times during the last six months of the calendar year, or if they have a written divorce decree, maintenance agreement, or separation agreement, there is a special rule that applies.
In this case, if the child received more than half of his or her total support for the year from one or both parents and was in the custody of one or both parents during the year, the IRS rules assume that the custodial parent (defined as the parent who has custody of the child for the greater part of the year) should get the exemption for the dependent. However, the parties may change this presumption and allocate the exemption to the noncustodial parent if either of the following are true:"
If parents want to deviate from the CP getting the tax credit they can but in most cases it is clear that the IRS rules assume the CP gets the tax credit because they have the child more than the other parent.