You're saying that, when you edit your video in Premiere Elements, files are automatically being created on your desktop? I have never heard of that in 10 years on this forum!
What operating system are you using?
What are the exact steps you're taking -- and what are the exact results you're getting? The more detailed the better, since we don't have the ability to actually sit at your computer with you and watch.
Thank you for so quickly gettng back to me. I am using OS X Version 10.5.8. I was happily trimming away and when I closed PE10 my desktop was covered in thumbnails of the scenes that I had been working on. What appears to be happening is that each time I trim a scene a 'clone' or copy of the scene, as trimmed, is duplicated onto the desktop. The first time this happened to me I rashly sent all of these thumbnails to the trash. Then found that PE10 wouldn't work any longer as it 'couldn't find the files.
Are you saving your project file to your desktop? That could be causing the problem, as the program may be auto-saving and creating render files to your desktop, since those files follow the project file.
Try saving your Premiere Elements project file to a folder on your hard drive. (In my books, I always recommend opening a new directory folder for each new project. It's just good housekeeping.)
Steve's Basic Training Tutorials... steps are the same for several versions
Bill Hunt on project setup http://forums.adobe.com/thread/919388?tstart=0