When is property abandoned and what can I do with it?

First, remind him again (preferably in writing) that he left some of his property at your house and that he can make arrangements to pick it up. You may want to follow up with a phone call. If he tells you that he doesn't want to pick it up, you can probably do what you want with it. But if he fails to answer you, keep it for a certain amount of time, perhaps several months and continue contacting him about it. This shows that you are making a good faith effort to return his property. If after more time has passed without an answer, go ahead and do what you like with the property. At that point, you can consider it abandoned. But keep records of your efforts to contact him, just in case he claims later that you took his property.