If you give the child a lump sum of $100K, that must be reported, even though you "saved" $10K per year. The gift doesn't occur until the money is actually transferred.
There's nothing to be scared of by the reporting requirement, it doesn't cause audits or raise your taxes.
However, if you want to give a child $10K per year but not actually let them have control until they are more responsible, you might consider a Uniform Gift to Minors trustee account.
https://www.investopedia.com/terms/u/ugma.asp
Or, you can contribute money to a 529 educational savings account in your name, listing the child as the beneficiary. When the child goes to college, they can withdraw the money tax-free for expenses, and if they don't go to college or have leftover after college, they can withdraw it and pay the taxes and keep the rest. And you may get a state tax deduction for the contribution (but not a federal tax deduction).
You may want to talk to a financial advisor about the best way to help your children or grandchildren while incurring the lowest taxes.
