Schematic illustration of the subhalo assignment in MORIA, which essentially follows the CONSISTENT-TREES method. Each circle indicates a host halo (red) or subhalo (orange) radius according to some radius definition. Halos are subhalos if their center lies within the radius of another halo with higher ﹩{V}_{\max }﹩. In this drawing, we assume that ﹩{V}_{\max }\propto R﹩ with the exception of halos 8 and 9, where the halo with the smaller radius becomes the host because it has a larger ﹩{V}_{\max }﹩. Halos 3 and 5 illustrate choices we need to make about sub-subhalos. In the case of halo 3, we assign halo 1 as the parent (rather than halo 2, which is also a parent). In the case of halo 5, the user can choose whether to assign the direct parent or parent-parent. In our catalogs, we have chosen to assign parent ID 4.