There are several perspectives to see this from. I see it from the "family" perspective.
Consider what your parents give you to be a gift. Plain and simple. So long as the amount is "less" than $15K in any one tax year, absolutely nothing concerning it needs to be reported to anyone at any level.
If you are eligible for any education credits on either the federal return (or state return if you are required to file one), then you can still take those deductions and credits. Your parents can't claim any such deductions or credits if they do not claim the children (and qualify to claim the children) as dependents on their own tax return. But you qualify if you claim your children as depends on your own tax return, regardless of who pays the qualified education expenses.
If your parents give you more than $15K in any one tax year, then they are required to file IRS Form 709 -Gift Tax return. Understand that *NO* *TAX* will be paid on the gift. The giver of the gift (not the recipient) is required to law to report it to the IRS *if* the amount given exceeds $15K in any one tax year.