"I did get a big return"--um, right, how? Did you claim them as "qualifying relatives" (even though they aren't) or as "qualifying children"?
Theoretically, if the mother and children lived with you for the entire year, the mom didn't work and you alone provided more than half of their total support, you could have claimed them as "qualifying relatives." At best, this allows you to claim the exemptions. You still must file as single, can't use head of household, can't claim the child tax credit or EIC. For 2-3 people, that's maybe a $1000 change to the refund. Most people wouldn't call that big, but it would be legal.
You see, when the shackup boyfriend provides more than half of the support and the kids lived with him all year, that means the two parents (custodial mom and non-custodial dad) didn't. The non-custodial dad can't claim them because he the children didn't live with him and mom can't sign a form 8332 because she isn't eligible to. Mom can't claim the kids because she has no income and either is a dependent of someone else (you) or didn't have a filing requirement at all. (Income has to be below $9350 and she doesn't claim EIC.)
To win the audit, you show how you provided the support.
Now, if you screwed up and claimed them as "qualifying children" when they have no legal or biological relationship to you, you screwed up big time. You can't file a return as head of household, claim the child tax credit and EIC when you have no relationship other than you might file for legal guardianship sometime in the future. In that case, you not only owe the big refund back, you will find yourself barred from claiming EIC for any child for 2 or 10 years.
Repeat, these are not your children. You aren't the bio-dad. You didn't marry the mother. You don't get legal recognition without actually doing something.