Hello JA Customer,
The rules for claiming HOH status are the same now as they were in 2008, and they have been the same for many years.
In order to claim HOH status, you must have a qualifying person who lives with you for more than half of the year, and for whom you pay more than half the cost of keeping up a home for that person. The problem in your particular case is not that you did not pay more than half the costs of keeping up a home for these children, but the children are not related to you in any way, which prevents you from claiming HOH status.
The HOH rules are confusing to many people on this issue, and so I can understand how you may have misinterpreted the rules and thought that you were entitled to claim HOH status. But this is not the case.
If your girlfriend was not required to file a tax return of her own, and if these children lived with you all year, and you provided for more than half of their total support, then you could claim them as dependents on your return under the rules for claiming a "qualifying relative", even though they are not actually related to you in any way. But the same "qualifying relative" rules do not allow you to claim HOH status.
Refer to IRS Publication 501 where it shows you in Table 4 that in order to claim HOH status, the qualifying person must be related to you in one of the ways listed under "Relatives who do not have to live with you". Those relationships include:
Your child, stepchild, foster child, or a descendant of any of them (for example, your grandchild). (A legally adopted child is considered your child.)
Your brother, sister, half brother, half sister, stepbrother, or stepsister.
Your father, mother, grandparent, or other direct ancestor, but not foster parent.
Your stepfather or stepmother.
A son or daughter of your brother or sister.
A brother or sister of your father or mother.
Your son-in-law, daughter-in-law, father-in-law, mother-in-law, brother-in-law, or sister-in-law.
So even though you may qualify to claim the children as dependents, they do not meet the definition of "qualifying person" for purposes of claiming the HOH status.