For those of you in the UK, as a law student myself who has also studied at American law schools, I think if I remember correctly that one automatically owns the copyright to their own work be it written, recorded on some form of media, performed etc. Check a Property lawyer if you are not sure.
The problem of course is often proving that you were the person who originally made the work and there are lots of documented cases of famous people being sued by unknowns who claim that they wrote something beforehand.
The copy rights to the recording itself are generally held by the PUBLISHERS NOT the engineers. They have automatic rights not to have the work reprouced etc etc etc without their permission (see warnings you always get on videos you buy or rent). The lyrics are usually the rights of the song writer/lyricist UNLESS (and this can happen to unwarey artists) they signed these away when they got that record deal they wanted so bad that they didnt read the small print!!!

The arrangement itself, to my knowledge can't be copy-writed and some companies actually specialize in exactly reproducing certain sections of a song so that an artist who would otherwise sample it doesn't need to pay royalties!
Talking of royalties remember if you use a sample check it out first!!!!! 'The Verve' lost ALL the money to their biggest hit and Brit number 1 'Bitter Sweet Symphony' as they used the tiniest sample of someone elses work without permission!!
If you have a record/publishing deal be aware of who owns the rights to what. You don't want a nasty shock.
I am sure Sound On Sound have an article on this in a back -issue. As I said, I would check this out with a property specialist before you rely on it.