Your parents allowing you to drive the car is legally known as a bailment. A bailment is a temporary placement of control over personal property to another person by the owner for a specific purpose. Your question implies that your parents anticipate only you driving the car. If they were to find out about your boyfriend driving it as a pizza delivery vehicle, that is very likely outside of the purpose of their allowing you to have possession of the vehicle. If your parents knew your boyfriend was driving this car, they could potentially report the car as stolen because it is no longer in your possession or theirs as your boyfriend has not received permission from your parents to drive their car.
Answered on Oct 17th, 2013 at 2:13 PM