Workstation Desktop Icon positions

I work in an enviroment where all computers are the same, and all personal files are stored on a network. So I can (and as a neccesity, do) log in on different computers all over the place. There are several that I regularly use depending on work assignments for the shift.
Because the desktop is where I have shortcuts, files, etc that i use often, I have them arranged in a very specific manner.
However, the positions of my icons are not saved in my network profile, and will not be how I like them, unless I manually move everything around. If I've never logged in on that particular workstation before, everything is a pile on the left side of the desktop.
My question is, is there a place where these positions are saved on the particular machine, such that I can migrate my layout from machine to machine? Does it maintain a specific file for each user, or does each machine have one file, that simply remembers everything every person who has logged in moved around?
I can't edit the registry or anything like that...

There are individual user folders under documents and settings, but i haven't found anything that screams out at me, insofar as icon location data...any help would be great, thanks!
And I will add that whenever I add something to the desktop, that icon WILL be on other computers i use, just not in the same place. Thanks!