If a grandparent pays for child's tuition, does someone get to declare that amount as THEIR contribution to support?Is it limited to $14,000.00 as a gift?

There are 3 gift giving exceptions, the annual 14k exclusion, education expenses, and medical expenses for others. Payments that qualify for the educational exclusion are payments made directly to a qualifying domestic or foreign institution as tuition for the education of an individual. 

 Do note that while the annual gift exclusion amount is $14k that doesn't mean there will be a gift tax to pay, it just means amounts over $14k per person must be reported.  the gift tax and the estate tax was reunified with an exclusion amount of $5.49 million for 2017. Gifts made during your lifetime will reduce your taxable estate. However, gifts in excess of the annual exclusion also reduce your estate tax exemption. Many people get worked up on the $14k amount but honestly it's normally just an extra form and taxes are only after $5.49mm in gifts over the annual exclusion are made.

So treat it if paid directly to school as tuition paid,  otherwise it can be a gift or it can be support, and it all matters your intent at time.

I appreciate your response, but the issue is that the mother of my grandson is claiming support of her child from the tuition paid by her parents, yet not claiming it as income to compute 'child support'. So my son, even though he has primary custody, isn't able to obtain any child support. (The childcare was instituted for the mother's benefit, although both benefit, but the child could also be in public school) Her family, like many wealthy people feel everyone is after their money, but in fact, the child is suffering by his father working extra and delaying finishing school to care for him.

the income from excess payments is reported on the students return...  the person who claims the dependent can only claim the scholarships and 1099's up to tution.... the student declares all excess paid.  You never will.