Yes, the round ends automatically if all divisees press the button "I am finished" in the bidding screen. The administrator can also manually close the round anytime.
As a divisee, you should press the "I am finished" button on the bidding screen when you are satisfied with your bidding for that round. This way the system can close the round as soon as everyone else does the same. Divisees who are not interested in any of the round assets should signal this by also pressing the "I am finished" button as this causes the system to know they have participated.
As an administrator, when you enter the rounds page you can see a "Close" button on active and extended rounds. If you click it and any of the round divisees didn't bid on it, the system will show a confirmation, telling you who are the divisees who haven't participated. The round will only be closed if you confirm.
Assets are distributed the same way as if the round closed on the set end date. This is to say, the mechanism through which the round is closed does not affect awards.