eZ Publish can handle multisites from one ezp installation. We have a client that has an ez publish installation with 6 domains (with different designs and content for every domain) managed from one admin area.
Like Andreas we have a number of clients where there are multiple distinct sites with their own domains running from a single eZ publish install. These sites share a database and the admin interface.
e.g.
http://www.nattrust.com.au/
http://www.melbournemaritimemuseum.com.au/
http://www.gulfstation.com.au/ http://www.ripponleaestate.com.au/
In general we run all sites that share a common eZ publish version off a single eZ publish source install. Individual clients have separate databases, settings and design diectories.
Most settings you need to be concern about can be found here: http://ez.no/doc/ez_publish/technical_manual/3_9/reference/configuration_files/site_ini/siteaccesssettings
Set MatchOrder to host to match on host name, then use HostMatchMapItems to map host names to siteaccess. If you want to use same database or not is up to you.
You also need to modify (override some of) the templates to avoid using the template_look class (the one you see if you click 'settings' from the front end or 'design' -> 'visual configuration' from the admin). Basicly since it's not multisite safe (it puts some of the settings in the override settings so they will affect all sites..).