400 words isn't a paper....its barely a couple paragraphs.... that said.....
I suspect that "co captain" issues arise on at least two occasions... first, if there is NOT a good working relationship between the two individuals and second....even in non emergency situations...someone needs to take the lead for a specific trip. Certainly input should be brought into play from the other "co captain" but in the end, only one pilots name appears on the flight plan as the PIC. I would think in a true co captaincy type situation "PIC" duties would be swapped on some sort of schedule. In other situations in might simply be a way to get the copilot a better pay scale.... the dynamics of this situation are endless, many good, but with the wrong relationship dynamic it could be very difficult.