You can't claim HOH unless you're claiming a dependent.
This should be spelled out in your divorce agreement. If it's not, every other year seems to be the norm for truly 50/50. If the child actually lives with one parent more than the other and there is no written agreement, the IRS considers the parent with whom the child spent more time to be the custodial parent. If both claim, there will be an audit.
The IRS is pretty clear as to who is the custodial parent even in joint custody cases:
"Custodial parent and noncustodial parent. The custodial parent is the parent with whom the child lived for the greater number of nights during the year. The other parent is the noncustodial parent."
"Equal number of nights. 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."
If the custodial parent (the one having more nights) waives claiming the child for a year, that waiver has to be filed in writing via a standard form that gets filed with his or her return.
For the year that my SD lived literally 6 months with us and 6 months with her mother, we both ran our numbers with and without her. Her mother stood to gain more with claiming her, so we let her claim her but she then had to pay us back what we calculated as our share.
More info:
http://www.irs.gov/publications/p504/ar02.html#en_US_2012...#