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Virtually any investigation involving dark matter halos relies on a definition of their radius, mass, and of whether they are a subhalo. The halo boundary is most commonly defined to include a spherical overdensity contrast (such as R200c, Rvir, and R200m), but different thresholds lead to significant differences in radius and mass. The splashback radius has recently been suggested as a more physically motivated (and generally larger) halo boundary, adding to the range of definitions. It is often difficult to assess the impact of a particular choice because most halo catalogs contain only one or a few definitions and generally only one set of host-subhalo relations. To alleviate this issue, we present halo catalogs and merger trees for 14 N-body simulations of LambdaCDM and self-similar universes. Based on ROCKSTAR catalogs, we compute additional halo properties using the SPARTA code and recombine them with the original catalogs. The new catalogs contain numerous variants of spherical overdensity and splashback radii and masses and, most critically, host-subhalo relations for each definition. We also present a new merger tree format where the data is stored as a compressed, two-dimensional matrix. We perform basic tests of the relation between different definitions and present an updated model for the splashback-spherical overdensity connection. The SPARTA code, as well as our catalogs and merger trees, are publicly available.