You will always have a black border when using HDMI, but once you set your overscan in the CCC by going to Graphics at the top/Desktops and Displays, then right click on the monitor picture at the bottom and configure. You will see a Scalings Options tab where you can adjust the overscan, once you apply and ok it, it will stay the full size of the screen from then on.
On a side note, for anyone still struggling with having a 4:3 image on lower resolution games, set your resolution to 1024x768 then go to configure display as just described,under the Attributes tab tick "scale image to full panel size" then ok and exit, you can now run at your proper resolution and all 4:3 games will now be 16:9.