The lingo is confusing... but when you surf the Internet, you never really go anywhere. And you're never really "on" a website.

Here's an example to clarify. When you tell your browser to "visit" Yahoo, it sends a request to the Yahoo.com web server, which returns a copy of the Yahoo home page to your browser. Your browser then renders the page on your screen (making additional requests for any embedded images), and waits for you to click a link on that page, or type in some other web address.

So you're only using a website's bandwidth while your browser is downloading a web page or image from that site. Even if you access a website that requires you to login, you're still not really "there". The illusion of a persistent connection to a website is accomplished by smoke, mirrors and software. Further, a website can't tell when you "leave", only that you requested a certain page (or sequence of pages) and then nothing further.

The situation you mentioned where you are downloading a large file from a site is no different, except for the extra time required to complete the file transfer. When the download is complete, your connection to that site is severed, and you needn't worry about using any bandwidth or other resources.