Who is responsible for any realized gains will depend on who the account holding the XOM stock is titled to. If it is your account that you are simply planning on using to pay for the grandchild's future college costs with, all realized gains on the account will be taxable to you and future payments for qualified educational expenses, providing you make them to the college, will incur no requirement for gift tax filing.

 But if this is within a custodial account, under Uniform Gift to Minors Act, the account belongs to your grandchild, realized gains of up to $1,700  will be first taxed to him ($850 not taxed and the next $850 taxed as ordinary income), with any amounts above this taxed at his parent's rate. And if titled this way, you cannot direct the use of the account for educational or any other use...it is the grandchild's to use as he sees fit once he reaches the age of majority for his state.

Have you considered using a 529 plan in saving for his future educational need?

BruceM