x authority problems

[Greg Fischer <gfischer4@mediaone.net>]

Given root access on a remote machine, I'd like to be able to execute an
x application on the remote machine's local desktop.  

For example, if I secure shelled into a remote machine as "user" and
"user" happened to be logged onto X, I'd like to be able to execute
"export DISPLAY=:0" from my secure shell terminal and then be able to
execute any X app and have it show up on user's desktop.

X security seems to be rather complicated.  Could someone point me in
the direction of some relatively concise documentation?  Or...

Another way to do it, I suppose, would be to see who presently is
running X and then do a "su $XOWNER".  Given root access, subsequent
commands would then work.  Is there a simple way to see who owns the X
process?

Any other solutions to the problem would be appreciated.  Thanks.

--Greg