So I am afraid my morning browsing habits include a visit to the Yahoo Comics page.
Comics and editorial cartoons - Yahoo! News (http://news.yahoo.com/comics/)

I usually open a dozen tabs or so. Recently part of this experience has started to include at least one spontaneous down load of a file named; "xd_arbiter.php" which is all of zero bytes in size. What is it? Is it potentially hazardous?....

Using latest version of Camino on a Tiger PPC Mac.

Tried to find a contact at Yahoo but their Contact/Help is more like a web version of Telephone Hell.

it's a problem with the Web server your contacting. It's using a server-side scripting language called PHP. For some reason, the server's choking and trying to send you the xd_arbiter script. Google "xd_arbiter.php" and you'll see your problem isn't uncommon, particularly with Facebook users, it appears. From what I've read, it doesn't appear to be anythng malicious.

Thanks for the explanation. I did find in my searches a big-league connection with UK Facebook but litle or no mention outside of that.

For me it happens only when visiting Yahoo. I do reset Camino at least daily, usually after Yahoo misbehaves. Have not signed into Facebook in a very long time, have Flash Cookies disabled, so at least in this case the connection seems to be with the Yahoo server not Facebook.

As you say it does not appear to be malicious but it is certainly annoying.