As has been indicated, the right belongs to the person who created it. The "registering of the right" originally was intended to encourage publication, so in some cases the mere existence of a work, and ability to prove that it existed, has had little standing in arguments in court. The "created work" needs to be made accessible to at least some others for it to have a really good chance of being recognized.

Be ABSOLUTELY SURE that any CD(s) that you put your songs on bear the © mark and date, along with the identification of the person claiming copyright (=creation right).

For a text work, registering the copyright with the appropriate agency (LOC in the US) is important, but for a music/performance work it probably does a lot more good to make sure it gets registered with the people who make a business of collecting the royalties. A clinker, however, in registering with the "performance arts" people is that your registration can imply that you accept their customary business practices - i.e. that you agree to allow anyone who wants to to "cover" your songs if they're willing to pay the going rate for the license. There are also cases in which people have signed over their rights in exchange for minimal payments, so read the fine print very carefully.

You should be strongly encouraged, as well, to "publish" a written lyric^© and notation^© for any CD issue as well. Otherwise your claim is only that no one else is allowed to play the same wrong notes that you played. For best likelihood of recognition in a dispute in court, there should be some "public access" to the written work as well, but you can reasonably limit the distribution to very few people. (A rejection letter from a publisher might meet the intent.(?))

If your stuff is any good, be assured that someone will steal it. The proof of ownership just gives you a fighting chance to make them pay you something for the theft use of your work.

I think. ... ?

John