The unasked question is "can my girlfriend claim my kids?". The answer is yes, no & maybe.
She can only claim them if she lived with them all year. Even then, she can only claim them as "standard" dependents for the $3800 exemption (deduction). Because they are not related to her, she cannot claim them as "Qualifying Children" for EIC, child tax credit or Head of Household filing status.
A person can still be a standard dependent (Qualifying relative in IRS parlance, even though they do not have to actually be related), if not a Qualifying Child, if he meets the 6 tests for claiming a dependent:
1. Closely Related OR live with you ALL year
2. His/her gross taxable income for the year must be less than $3,800 (2012)
3. You must have provided more than 1/2 his support
In either case:
4. He must be a US citizen or resident of the US, Canada or Mexico
5. He must not file a joint return with his spouse
6. He must not be the qualifying child of another taxpayer
He must have a US social security number or tax identification number (TIN)
In addition to the above requirements, to claim your boy/girlfriend's children, they must meet all of the above requirements and:
--- your boy/girlfriend must not be required to file a return,
--- he/she does not file a return claiming the children