Here is the exact answer from the IRS FAQ website:
Question: For head of household filing status, do you have to claim a child as a dependent to qualify?
Answer: In certain circumstances, you do not have to claim the child as a dependent to qualify for head of household filing status; for example, a custodial parent may be able to claim head of household filing status even if he or she released a claim to exemption for the child.
This means that in a divorce or paternity agreement you should designate if one parent will still have the right to qualify for Head of Household, even if the other parent is being given the dependency exemption.
For a further discussion on who gets the dependency exemptions in a divorce read our previous post: Child Tax Deductions: Who gets them in a Divorce?