An understanding of ownership entails the recognition that ownership can be transferred permanently and the ability to differentiate legitimate from illegitimate transfers. Two experiments explored the development of this understanding in 2-, 3-, 4- and 5-year olds, using stories about gift-giving and stealing. The possibility that children use simple biases to identify owners, such as a first possessor, current possessor or a loan bias, was also investigated. Five-year olds appropriately acknowledged a permanent transfer of ownership in the case of giving but not stealing. Four-year olds allowed permanent transfers but struggled to differentiate legitimate from illegitimate transfers. Many 4-year olds allowed adults, but not children, to keep property that had been stolen. Two- and 3-year olds exhibited a first possessor bias for both stories. We conclude that, by 5 years of age, children possess a mature understanding of ownership transfer whereas younger children are prone to biases. (Contains 3 tables and 2 figures.)