Emails Retained on Server

I am using Windows 7 Home Premium and just installed Windows Live Mail.

My ISP is Time Warner Roadrunner POP/SMTP Server. On my Vista computer, Windows Mail emails were saved on their server until I downloaded them to my computer. Then they were saved on my computer until I deleted them.

It sounds like WLM saves them on their server. But they are still on that server after Time Warner downloads them to me.
I am trying to understand how it works.

I see that I can uncheck Leave Messages on Server.
Does that remove it from the Roadrunner server?

Does it stay on the Windows Live server? If so,
How long does it stay there if I do not delete them?
Is there a maximum size for the stuff on that server?

Thanks, cb