Another thing I have learned. “Computer“, “Home” and “Trash” won’t go away from the Desktop unless You do this:
Open gnome-terminal and issue this command:
Now click on the arrow on the left hand side of the Apps, it will expand it. Now find and click on the arrow on the left hand side of the Nautilus to expand it, now find and click on desktop. In the right pane of the gconf-editor window You will see few entries with the ticks.
Check out what happens if You untick them – so it looks like this: