I think if you look in c:\users\{yourname}desktop and compare it with c:\users/allusers\desktop you'll find them to be identical. If you then delete the unwanted icons from the AllUsers desktop file as well as your own, you won't see them again on your Desktop.
I'm posting from a Linux machine at the moment so I can't be sure of this but I think you might need to open up the hidden files to see the AllUsers account folders. from that, select the View menu in Windows Explorer then over to the right click on Options and when the All files and folders bit shows, click that. Then in that View menu tick to Show Hidden Files and Folders and untick Hide System Protected Files and Folders. Reverse that later or you'll see shadow...