how do I apply a copy of my avatar to my desktop?

Answer 1

I don't think right-clicking the image from the avatars page will help you, as the avatar there is Flash content, not an image. Instead, try this:

1. Display the avatar in MSIE.
2. Press Alt/PrtScrn to copy the displayed image to the clipboard.
3. Open an image editor, such as Paint Shop Pro, and paste the image from the clipboard.
4. Crop the image to get only the avatar.
5. Save the image file to your hard drive.

To set the image as the desktop background (wallpaper), then select the image file you saved in Step 5 above from the Display Properties dialog (right-click the desktop, click Properties, and click the Desktop tab.), then click Apply and OK.

Answer 2

If you want it to be your desktop background here's how to do it on a PC.
Right click on the image and click "Set as desktop background" and it'll automatically save as your background.

If you just want to save the file onto your desktop, right click on the image and click on "Save image as" and save it to your desktop.