Taking Box Sync off old computer by logging out?

I posted this question a few days ago and did not receive a response, so want to ensure that this question is seen: 

I am transitioning from an old computer to a new one, and want to ensure that my Box account is no longer linked to the old computer. Is it enough to log out of Box on the old computer's Box Sync application, or do I need to uninstall / do something else? 

(Apologies for the urgency)