Copyright is not something you can take away. It exists from the moment you create something creatively and originally.

You can however license someone to use something that is protected by copyright. This is what licenses do; they give you a license to use the content.

This is exactly what CC0 tries to do, it works around the fact that you cannot (easily) give away or stop copyright, but can state that you distance yourself from all the rights that come with having the copyright. See also: http://creativecommons.org/about/cc0