Hi Eric There are many ways this can happen, I can only say what I would do. If you were dealing with me and I had complete songs you would be the arranger you would own the copyright in your arrangement. I would own the copyright in my song, I would then have an agreement to pay you a fee for the work depending on the complexity of the arrangement work, the number of charts you had to write etc. And a further fee for the exclusive use of your arrangement to make a recording if I decided to do that.
If I had for example a verse chorus structure that needed a bridge and you composed the bridge, or you had a riff that was the main hook of the song and I wrote a melody and lyric based around that hook and chord progression, then that would be a co write you would then own 50 percent of the copyright in that song. I would expect you to chuck in the arrangement rights as part of your 50 percent.
I think the main thing is to all be up front and agree everything at the start. Here is a primmer on a do it yourself agreement
http://www.music-law.com/musiccontracts.html
BTW how good is your arranging any sample we can hear?
Cheers