  We find that infalling dark matter halos (i.e., the progenitors of satellite
halos) begin losing mass well outside the virial radius of their eventual host
halos. The peak mass occurs at a range of clustercentric distances, with median
and 68th percentile range of 1.8 +2.3/-1.0 R_(vir,host) for progenitors of z=0
satellites. The peak circular velocity for infalling halos occurs at
significantly larger distances (3.7 +3.3/-2.2 R_(vir,host) at z=0). This
difference arises because different physical processes set peak circular
velocity (typically, ~1:5 and larger mergers which cause transient circular
velocity spikes) and peak mass (typically, smooth accretion) for infalling
halos. We find that infalling halos also stop having significant mergers well
before they enter the virial radius of their eventual hosts. Mergers larger
than a 1:40 ratio in halo mass end for infalling halos at similar
clustercentric distances (~ 1.9 R_(vir,host)) as the end of overall mass
accretion. However, mergers larger than 1:3 typically end for infalling halos
at more than 4 virial radial away from their eventual hosts. This limits the
ability of mergers to affect quenching and morphology changes in clusters. We
also note that the transient spikes which set peak circular velocity may lead
to issues with abundance matching on that parameter, including unphysical
galaxy stellar mass growth profiles near clusters; we propose a simple
observational test to check if a better halo proxy for galaxy stellar mass
exists.
