  In this study, we perform a halo-finder code comparison between Rockstar and
CompaSO. Based on our previous analysis aiming at quantifying resolution of
$N$-body simulations by exploiting large (up to $N=4096^3$) simulations of
scale-free cosmologies run using Abacus, we focus on convergence of the HMF,
2PCF and mean radial pairwise velocities of halo centres selected with the
aforementioned two algorithms. We establish convergence, for both Rockstar and
CompaSO, of mass functions at the $1\%$ precision level and of the mean
pairwise velocities (and also 2PCF) at the $2\%$ level. At small scales and
small masses, we find that Rockstar exhibits greater self-similarity, and we
also highlight the role played by the merger-tree post-processing of CompaSO
halos on their convergence. Finally, we give resolution limits expressed as a
minimum particle number per halo in a form that can be directly extrapolated to
LCDM.
