The entire industry has always been structured for separate music publishers. Songwriters ought to be informed they need to set up a publishing company before they register their copyrights.
Unfortunately, finding information about how to actually get paid is very hard to find on the internet. I set up a forum 15 years ago addressing this:
https://web.archive.org/web/20040502...ndex.php/f/12/
The current version is:
http://www.recpit.net/ It isn't very active but could be!