The creators have the exclusive right to determine who can produce copies of their song, for example to create records. This right can be granted to others by giving out a mechanical license, which is done in exchange for a monetary payment (mechanical royalties).
Whenever a record label or performing artist wants to record a song that they do not own, they have to get a mechanical license from the people that do. Always.
All decisions regarding the composition can only be made when agreed upon by all copyright owners. As mentioned before, the ownership and control of copyright can be transferred to others. Generally, songwriters get a specialized third party, namely a publisher, to control and manage their songs. In exchange, they get a cut of the royalty streams which they help generate with the repertoire.
Writer-publisher splits tend to range between 50%-50% and 70%-30%, depending on the clout of the artist and sometimes even on the relevant country’s regulations.