Cumulative size-frequency distributions N(>D) resulting from two Monte Carlo collisional models: the main belt and Julia family (left column); the main belt and the family without the largest remnant (89) Julia (right column). The main belt SFD is plotted in blue and the family SFD in red; the respective initial conditions are plotted in cyan and yellow, and the observations in gray; the bend at around D ≃ 1 km is mostly due to the observational incompleteness. The situation at time t = 30 Myr (top row), and t = 520 Myr (bottom row) is shown. There are always 10 runs with a different random seed in order to see lower probabilityevents. The first model demonstrates that the Julia family is by no means an exception; the second model shows that small fragments (from a single breakup) decay quickly within a few 100 Myr at most.