I live with my girlfriend. We have 3 kids. She makes more money than me. Can I still claim my kids on my taxes?

[xmasbaby0]

If you are a non-married couple who live together then only one of you can claim the child(ren) and the one not claiming the child does not enter anything at all on their tax return about the child. 

[Opus 17]

If you are both biological parents of all three children, then you can split the children any way you like, as long as each child is only claimed once.  Due to a quirk in the dependent interview, it is best if the parent who is not claiming the child does not even list them in their return, and the parent who is claiming a child should answer "no" to the question about a custody agreement (that only applies to divorced parents).

What way to claim the children gives the best refunds needs to be tested.  If you are eligible for EIC, it might be better for the lower income parent to claim at least one or two children.  But you need to test the combinations for yourself. 

[Hal_Al]

If you and the other parent live together, either one of you (but not both) may claim any child. You may decide between you which one will claim which children. Only if you can’t agree, do the IRS tie breaker rules apply, to see who has first choice (and yes, it's the parent with the higher income).

It may be worthwhile to prepare trial returns, both ways,  to see which way the family comes out best. This tool may be useful: https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1.

As others have said, if you are not claiming a child, do not enter that child in TurboTax.  The interview is confusing (it's designed for divorced parents, who are allowed to split the child). The second parent should not enter the child, at all.

[TomD8]

Another wrinkle is that the parent who has the higher income can usually file as Head of Household (the other parent files as single).

[Hal_Al]

In order to claim Head of Household, the taxpayer must be claiming at least one of the kids (a "qualifying person")

[TomD8]

Correct.  And in most cases the lowest combined tax bill is achieved by "splitting" the kids between the two returns.