There is a very simple way to hide the login link at the top of the DotNetNuke home page.

You do not need to edit a style sheet or any such.

Simply go to Site Settings >> Security Settings

check the box that says " Hide Login Control? "

It seems that every body is looking to hide the dotnetnuke login link but apparently this is not documented.

Just about every solution I found on the Internet involves editing the css file.