The radio usually pays a license fee to the local performing rights authority and the authority then pays a percentage of license fees to the artists. That’s a very watered down version, but essentially how it works.
The authority then handles the back end admin of managing who gets paid, different artists and their labels have different requirements and royalties and all of that is often negotiated through deals, so there are many many variables to how it works. But as far as the radio station is concerned, they pay a license fee to be allowed to play the music, then the authority takes care of the rest.
I believe the radio station also sends a report to the authority on a regular basis to show what was played when to determine actual royalties for each artist.
Tldr: the radio station pays a fee to a regulating authority to play all music the authority represents, then sends its playlist to the authority regularly. The authority then pays artists. The artists and labels sign with the authority to manage royalties.
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