Generally authors automatically own the copyright to any work they originate, assuming that is they do not sign over the copyright to another.
In the UK and many other countries, there is no need to make a formal registration of ownership, however registration may assist in proving ownership, especially if the work created is to be sold.
If an author gets paid to make a work for someone else, the person who pays for making the work will often get to own the copyright, unless specific provision is
made in the form of a signed
contract agreeing ownership.