Most of the small companies just create designs and do not apply for a copyright. How does copyright come into play if the designer or the company has not copyrighted their work?
First of all, it depends on the region but the most common of all copyright "laws" is the Berne Convention for the Protection of Literary and Artistic Works.
Which basically states that you automatically have the copyright to any work you create even without notice on the work itself. There isn't an official register of copyright.
I started with "it depends on the region" therefore here is a List of parties to international copyright agreements
That's about all there is to it from what I know, you can also apply for trademarks and patents if you have something that qualifies. Also, if you are really worried about intellectual property, you might want to seek some legal advice from a lawyer that specializes on these kinds of things.
This may be a long ago answered question but on reading the content I noticed there was no reference to "file info". This exists in AI (found under File> file info) and mirrors the way photoshop users add metadata to each file so that it follows the digital version at least where ever that goes. No protection from thieves as such but it labels your work as yours and enables you to tag the work as copyrighted with your details and much more. Apologies if you know this it can help as far as posting work on the internet though of course will not be displayed with printed work and then Alins input is correct.