They own the copyright in many instances. Yes, it is copyrighted material - with an OSS license that dictates the use. Violations of the GPL (for example) are copyright violations. The GPL is a form of copyright.
They are, in turn, owned by corporations. Don't scoff at the word immediately, as there are many types of corporations. The term just means that they're incorporated entities, often non-profit organizations.
The author technically owns the copyright. If I violate the GPL, you can't do anything. The copyright owner(s) have to take legal action. You have no standing. It was never your property, you were just given a license to use it (with various terms). Again, that is copyright.
So, it's a whole big mess. Trying to find all the copyright holders (since 1978, copyright is automatic, assumed at the moment of inception) would be impossible. I believe some projects have terms where you give an unlimited-use license to the project when you submit code to the project.
Which is to say, yes... Yes, there are owners.
By the way (US laws, but many other nations follow suit) you don't have to apply for a copyright anymore. That changed in 1978. But, if you register your copyright, you can sue for damages. Otherwise, you can only sue to make them stop using your property.
Below is just one example, specifically with GNU licenses... (CTRL + F for 'copyright' if you want to not read the whole thing.)
www.gnu.org