Remember that for appreciated stock, the original basis is retained. E.g. if you bought the stock for $1000 and it's now worth $14,000 and you gift it to your child. If that child sells it for $14,000 they have a $13,000 capital gain.
The tax rate on that CG depends on, well, this:
Tax Topics - Topic 553 Tax on a Child's Investment Income
Which doesn't apply for gifted stock to other folks, but the OP mentions kids.
Depreciated stock gifts are a little different. Usually it's better to just sell the stock (retaining the gain) and gifting the cash since the new basis is the price at the time of the gift.
And finally, remember this is different from giving appreciated stock to a charity, but that's another issue.