I've also participated in round robins where each member creates her own center and then the others add the borders, sometimes following a theme and sometimes not. They are really fun and you get some beautiful quilts.
However, we've found that a Row Robin is an easier project. The first person makes a row with whatever blocks, colors, theme, etc. she chooses. (In last year's Row Robin some members had themes like cat blocks, house/tree blocks, stars, and wildflowers. Others had particular color preferences.) Then everyone else adds a row following the originators wishes. The best thing about making rows is that much of the math is eliminated. The row each person makes will only be as wide as the first row, with the same number of blocks. And the height of the row will be the same or at least proportional to the first row. So there's much less math to work out than when you have to add a complete border all the way around.