BWA's answer is wrong, regarding tiebreaking. IRS Publication 501 clearly states:
"If the child lived with each parent for an equal number of nights during the year, the custodial parent is the parent with the higher adjusted gross income (AGI)."
And
"If the child lived with each parent for the same amount of time, the IRS will treat the child as the qualifying child of the parent who had the higher adjusted gross income (AGI) for the year"
