The artist use to get something like 5 cents every time the recording was played over the air. Is this no longer done?
The publisher (the one who owns copyright, not the singer). Publishing originally was split between ASCAP and the listed songwriter(s).
ASCAP refused to record R&B (originally called “race” records), C&W (originally called “hillbilly” records), and their byproduct Rock and Roll. BMI would.
When BMI published songs suddenly topped the charts by giving the public songs that ASCAP wouldn’t, ASCAP alleged payola (which had been in the industry since day one and remains there TODAY).
Sometimes publishing is transferred from someone to someone else. Often through crooked contracts. Allen Klein stole the Rolling Stones’ back catalog. Ahmet Ertegun stole the Stax catalog.
I don’t recall the exact circumstance of the Beatles losing publishing on their songs (recall that Michael Jackson purchased them at one point, after Paul McCartney was telling him own buying back catalogs was a good investment, Paul had bought the Buddy Holly catalog).