  Profiles of dark matter-dominated halos at the group and cluster scales play
an important role in modern cosmology. Using results from two very large
cosmological $N$-body simulations, which increase the available volume at their
mass resolution by roughly two orders of magnitude, we robustly determine the
halo concentration-mass $(c-M)$ relation over a wide range of masses, employing
multiple methods of concentration measurement. We characterize individual halo
profiles, as well as stacked profiles, relevant for galaxy-galaxy lensing and
next-generation cluster surveys; the redshift range covered is $0\leq z \leq
4$, with a minimum halo mass of $M_{200c}\sim2\times10^{11} M_\odot$. Despite
the complexity of a proper description of a halo (environmental effects, merger
history, nonsphericity, relaxation state), when the mass is scaled by the
nonlinear mass scale $M_\star(z)$, we find that a simple non-power-law form for
the $c-M/M_\star$ relation provides an excellent description of our simulation
results across eight decades in $M/M_{\star}$ and for $0\leq z \leq 4$. Over
the mass range covered, the $c-M$ relation has two asymptotic forms: an
approximate power law below a mass threshold $M/M_\star\sim 500-1000$,
transitioning to a constant value, $c_0\sim 3$ at higher masses. The relaxed
halo fraction decreases with mass, transitioning to a constant value of $\sim
0.5$ above the same mass threshold. We compare Navarro-Frenk-White (NFW) and
Einasto fits to stacked profiles in narrow mass bins at different redshifts; as
expected, the Einasto profile provides a better description of the simulation
results. At cluster scales at low redshift, however, both NFW and Einasto
profiles are in very good agreement with the simulation results, consistent
with recent weak lensing observations.
