What you and Gamie bj are describing to me is called a round robin. Also a fund thing to do with your quilting friends. There are various ways I think of doing a friendship quilt. I think of each of you doing some blocks that have a white or neutral area that each person can sign their name and you exchange these. You can pick one pattern that you all do the same block or each person can do a particular block with some designated color or theme so they would relate to each other once put into a quilt.
It is your group and your fiends, so do what you want and enjoy the process.
Here is something of the history:
http://www.womenfolk.com/quilting_hi...friendship.htm