  Dark matter subhalos are the remnants of (incomplete) halo mergers.
Identifying them and establishing their evolutionary links in the form of
merger trees is one of the most important applications of cosmological
simulations. The Hierachical Bound-Tracing (HBT) code identifies halos as they
form and tracks their evolution as they merge, simultaneously detecting
subhalos and building their merger trees. Here we present a new implementation
of this approach, HBT+, that is much faster, more user friendly, and more
physically complete than the original code. Applying HBT+ to cosmological
simulations we show that both the subhalo mass function and the peak-mass
function are well fit by similar double-Schechter functions.The ratio between
the two is highest at the high mass end, reflecting the resilience of massive
subhalos that experience substantial dynamical friction but limited tidal
stripping. The radial distribution of the most massive subhalos is more
concentrated than the universal radial distribution of lower mass subhalos.
Subhalo finders that work in configuration space tend to underestimate the
masses of massive subhalos, an effect that is stronger in the host centre. This
may explain, at least in part, the excess of massive subhalos in galaxy cluster
centres inferred from recent lensing observations. We demonstrate that the
peak-mass function is a powerful diagnostic of merger tree defects, and the
merger trees constructed using HBT+ do not suffer from the missing or switched
links that tend to afflict merger trees constructed from more conventional halo
finders. We make the HBT+ code publicly available.
