Simply, you are not required to claim your children as your dependents for tax purposes.
HOWEVER, and this trips a lot of young people up, from THEIR perspective, there is a question on the tax return that asks CAN someone else claim them? So they have to answer "yes" regardless of your action!
The IRS was smart enough to ensure that your decision doesn't confer any benefits on your children. For example, they are not eligible for the stimulus payments because you CAN claim them; whether you do is immaterial to the IRS.
