Children don't have owners, they have parents -- and the determination of responsibility is much less clear than your glib comment implies.

For example, is liability held by the biological parent, or by an entity acting in loco parentis? The distinction is crucial, as it is similar to the difference between an owner of a car, and a renter of a car.

With pets, again, if I lease or rent a pet it is not the case that the owner is necessarily responsible for the pet while I have possession. They may, but they also may not -- and it's this uncertainty which drives much frustration with tort law.

Guardianship is probably the word in the case of children ;-)