Are you saying that some sites don't fill the monitor completely, leaving black borders?
What browser are you running? What type of sites are you talking about?
If the site is playing Flash, QuickTime, or other video player, the display will change according to the settings for that player, and how the content was coded (or shot) by the writer/producer.
Unless you're talking about watching HDTV using the HDMI input on the monitor? Then it's a different explanation, but in any case, I do not believe the issue is the monitor.
FW