The first song you write with someone is like a first kiss. The songs (or the kisses) that follow might be better for other reasons, or you might never want to write another song with that person again. Either way there's no song like the first song. There just isn't.
The term "Publishing Administration" gets thrown around a lot in the music industry, and if you're a songwriter, it's critical that you understand what it means, how it works, and what your options are.