I was talking about morality, not legality. Legality is never cut and dry.
So, in answer to your question, being a big fan of Negativland and MACOS and fair use, the "new" artist would be the one receiving the royalties, as they are the one who "wrote" the new song. Of course, if it's as unoriginal and crappy as "Ice Ice Baby", I'd work outside the system and insult and deride the artist until they stopped playing it.