  In the far future of an accelerating LCDM cosmology, the cosmic web of
large-scale structure consists of a set of increasingly isolated halos in
dynamical equilibrium. We examine the approach of collisionless dark matter to
hydrostatic equilibrium using a large N-body simulation evolved to scale factor
a = 100, well beyond the vacuum--matter equality epoch, a_eq ~ 0.75, and 53/h
Gyr into the future for a concordance model universe (Omega_m ~ 0.3,
Omega_Lambda ~ 0.7). The radial phase-space structure of halos -- characterized
at a < a_eq by a pair of zero-velocity surfaces that bracket a dynamically
active accretion region -- simplifies at a > 10 a_eq when these surfaces merge
to create a single zero-velocity surface, clearly defining the halo outer
boundary, rhalo, and its enclosed mass, mhalo. This boundary approaches a fixed
physical size encompassing a mean interior density ~ 5 times the critical
density, similar to the turnaround value in a classical Einstein-deSitter
model. We relate mhalo to other scales currently used to define halo mass
(m200, mvir, m180b) and find that m200 is approximately half of the total
asymptotic cluster mass, while m180b follows the evolution of the inner zero
velocity surface for a < 2 but becomes much larger than the total bound mass
for a > 3. The radial density profile of all bound halo material is well fit by
a truncated Hernquist profile. An NFW profile provides a somewhat better fit
interior to r200 but is much too shallow in the range r200 < r < rhalo.
