Marion,

gonce the song is published you cannot prevent anyone recording it themselves, or using your recording in advertising or in film, theatre etc. They will owe you royalties for mechanical copyright or performing rights respectively, but that's all.

As to why one might want to start their own publishing company: I am guessing here, and stand to be corrected by others, but from what little I know there are precious few benefits for the normal "punter" like you and me. But IF you make it big, you might want to negotiate distribution deals with distribution companies; or you might want to have other artists under your label. Those two are the only reasons I can think of. As I said, nothing really in it for normal mortals.