But the standard language defining "possession" is "subject to the immediate dominion and control". In other words, it doesn't have to be "on" you, but close enough that you could lay hands on it and use it. "Close enough" is a sliding concept, depending on where you are. If you're by yourself, walking around in a shopping mall, it pretty much means "on" you. If you're in the basement of your house, the third-story bedroom might be "close enough". The issue is your ability to exercise "immediate dominion and control", not necessarily proximity.
There, is that clear as mud?