General rule. The parent who has custody of the child for the greater part of the year (the custodial parent) is generally treated as the parent who provides more than half of the child's support.
If the parents are divorced or separated during the year and had joint custody of the child before the separation, the parent who has custody for the greater part of the rest of the year is considered to have custody of the child for the tax year.
Example : Under the terms of your divorce, you have custody of your child for 10 months of the year. Your former spouse has custody for the other 2 months. You and your former spouse provide the child's total support. You are considered to have provided more than half of the support of the child. The excemption would be yours.
Exception:The noncustodial parent will be treated as providing more than half of the child's support if:
The custodial parent signs a written declaration, discussed later, that he or she will not claim the exemption for the child, and the noncustodial parent attaches this written declaration to his or her return,
The custodial parent may use either Form 8332 or a similar statement to make the written declaration to release the exemption to the noncustodial parent. The noncustodial parent must attach the form or statement to his or her tax return.
The exemption can be released for a single year, for a number of specified years (for example, alternate years), or for all future years, as specified in the declaration. If the exemption is released for more than one year, the original release must be attached to the return of the noncustodial parent for the first year, and a copy must be attached for each later year.
So in other words...it may sound ridiculous to you but it doesn't to the IRS since your ex probably pays more than 433.33 a month for the child anyway.