the legal right to reproduce your work

Who registers the copyright for my book?

Your publisher will do this at some point after you sign your publishing contract.

Does my publisher own my copyright after I sign my publishing contract?

No (unless you are publishing this book as “work for hire,” meaning that you wrote this book as an assignment from the publisher). You own the copyright to your book. The publishing contract you sign gives your publisher permission to publish your book exclusively until it goes out of print, but it does not transfer ownership of the copyright to them (unless you are doing work for hire).