Why is my zenid always there?

My zen cart store is installed on a web host, and the OS is Linux. Everything works fine till now. But I found that the 'zenid=xxx' is always there in the URL string while using IE/Chrome. But it only appear once on first entry while using FireFox3.5.

On some posts I read that the error or unwritable "Confuguration | Sesssions | Sessions Directory" may cause this problem. So I change and check the directory and chmod. It should be right now, but the 'zendid' have still not gone.

It's more weird that on my own PC(OS: win Xp), I set the "Confuguration | Sesssions | Sessions Directory" to be a directory not existed, but the 'zendid' parameter still seem ok on all of the Firefox/IE/Chrome.(It means it appear once, then gone.)

Is there any clues that i missed about this?

Thanks for any help!

The zenid will disappear only if the browser is configured to allow a Session Cookie to be set.
If your browser's security settings are set to prevent cookies or session cookies from being set, then the zenid will continue to appear on every page.

If it's working on some browsers but not others, then the problem is NOT related to your Sessions Directory setting, or any other Zen Cart setting.

Thanks to DrByte!
I also guessed it should be about the browser. But I've double checked the cookies configuration of IE and chrome to be acceptable for Session Cookie. However, I found nothing wrong.
Then I installed a zen cart on my own PC as I mentioned above(sorry but i missed some sentences and caused confusion), the 'zenid' seems ok on all browsers.

Now i find that the cookies from my website on Chrome doesnt contain one named 'zenid', which appears in the 'Show cookies' from Firefox. But the 'zenid' cookie(should i call it this way?) also appears from my local site on Chrome. But I just could not find out why.

I think i've gone too fat on this problem and give up temporarily. If I figure it out some day, I'll post it up here.