There's always a cutoff just due to practicality. If you give a friend $5 probably neither of you filed taxes for that. If you give a friend $10m, well, the IRS will probably notice that one.

(in the case of a gift tax the cutoff is $14k and yes it applies to your children, see: https://www.irs.gov/Businesses/Small-Businesses-&-Self-Emplo... )