I currently help to administer a website though another hosting service. They are in the process of moving and really don't want to host the website any longer. Is it possible to transfer it to be hosted by Zymic. It has its own domain name as well btw - www.kols.org.

Yeah it's possible to transfer it but you have to do all the transfering.

Start up a hosting account.
Download all of your Files from your old ftp.
Upload all of your files to the new site.
Hopefully if you have Forums, or anything that needs a database, you know how to change the username and password, and Database name.
Add a custom Domain.

Then your set.