I saw a talk (filmed) last year at an independent movie house by a very knowledge Beatle historian. It was called Deconstructing the Beatles: Yeah, Yeah, Yeah. This particular talk focused on their breakout year of 1963. What they packed into that year was phenomenal. Part of that, was writing many, many songs that were given away to other artists...which, in large part, became hits. Here is the brief trailer where he mentions that:
https://www.youtube.com/watch?v=6nJRn2QN-W0
They gave the Stones their first UK hit with “I Wanna Be Your Man.”