Forum Moderators: Robert Charlton & goodroi
It's not important if the duplicate content is hosted on the same server or a different server. If it's duplicate, it's duplicate. End of discussion.
Best practice is to decide for ONE domain to be the main address (in case of .co.uk and .com I would opt for the .com if your business is international), and to set up "permanent redirects" (often called 301 redirects) from the additional domains (often called "vanity domains"). This makes sure you host only ONE copy of the content, which will avoid penalization by the search engines, but still allows for type-in traffic.
If your host charges you to setup redirects (anything more than a minimal admin charge), then just find somewhere you can park your domains and setup the 301's yourself.