If a child buys and gives a Talis as a present with money he earned, is the adult that wears it doing a Mitzvah D'oraisa each time ?
A Talis requires Tzitsis only if it is yours, but not if it belongs to someone else. [Shulchan Aruch 14/3]
In Choshen Mishpat [235/1-2]it is clear that M'dirabonon a child can sell or give a gift, but only if he doesn't have a "Apetrapus" manager.
The questions are:
1 - Does a child living by his parents have the same din as a child with an apitropus?
2 - Even if he can give a present, does that mean that it is considered the receivers for a Mitzva D'oraisa?
We do find by the esrog that receiving an esrog from a child can be problematic. [see Shulchan Aruch 658/6]