I claim and support my grandchildren. Their parents may have to start paying support, and think that they are entiled to my taxes. I say that they are not, but what do you say?

IRS has strict rules and regulations concerning who can claim dependent children for income tax purposes. Claiming Dependents - Tax Laws for Claiming Dependents on Your Tax Return

Do the grandchildren live with you, and not with their parents? If so you may have a case. But if the children live with their parents, then the parents' right to claim the chldren as their dependents supercede yours, even if you are providing the majority of financial support. Please provide further details as to whom the children live with the majority of the time.