The file is on the top level of the Mac HD. I am pretty sure it's the culprit due to the messages in Console. it shows the file constantly accessing the Internet. I can also trace the start of the problem back to when Norton was un-installed.
I ran the Symantec removal tools - but don't think they got rid of the file. However, using the
sudo rm -rf /.SymAVppcFile
command seems to have worked!!!
It currently looks like the disk is acting normally and not filling up on it's own.
So many thanks for the help.
Please note that I just edited the command in my original post. The r isn't hurting anything when the command is typed correctly, as you did, but it's a typo waiting to happen. Doing so allows me to remove the disclaimer, since an errant space will just produce an error rather than deleting every file on your hard drive.