Asteroids from the synthetic AstDyS catalogue plotted in the proper semimajor axis a_p vs. proper eccentricity e_p (top panels) and a_p vs. proper inclination sinI_p planes (bottom panels). We show the identified asteroid families (left panels) with the positions of the largest members indicated by red symbols, and also remaining background objects (right panels). The labels correspond to designations of the asteroid families that we focus on in this paper. There are still some structures consisting of small objects in the background population, visible only in the inclinations (bottom right panel). These “halos” may arise for two reasons: i) a family has no sharp boundary and its transition to the background is smooth, or ii) there are bodies escaping from the families due to long-term dynamical evolution. Nevertheless, we checked that these halo objects do not significantly affect our estimates of parent-body sizes.