We study the coauthorship distribution by analyzing the number of coauthors on each paper published in Physical Review Letters and Physical Review for the last decade. We propose that the structure of the distribution can be understood as the result of a two-parameter Poisson process. We develop a dynamic model of dual mechanisms to simulate the personal and group collaborations. In this model, the single-author papers are portrayed as a leftover from the collaboration process. We also comment on the huge collaborations involving hundreds of coauthors.