Key points to bear in mind:
The IRS does not use common English words like married, child, relative, or lived with in the same way that normal people do. Read my blog post on IRS Double-Speak to understand better how the IRS uses these terms.
Sometimes a taxpayer may be eligible for more than one filing status, so keep in mind that, in general, the filing status pecking order is: MFJ > QW > HoH > S > MFS.
Allthough MFS is generally "the pits", if a married taxpayer does not want to file MFJ (e.g., because of domestic violence or abandonment), you should always check to see if s/he qualifies to be "considered as unmarried" by the IRS for the purpose of HoH filing status.
For more information on filing status, see this very helpful lesson, and also see the section on filing status in Pub 17.