  The evolution of marginally bound supercluster-like objects in an
accelerating LambdaCDM Universe is followed, by means of cosmological
simulations, from the present time to an expansion factor a = 100. The objects
are identified on the basis of the binding density criterion introduced by
Dunner et al. (2006). superclusters are identified with the ones whose mass M >
10^15 M_sun/h, the most massive one with M ~ 8x10^15 M_sun/h, comparable to the
Shapley supercluster. The spatial distribution of the superclusters remains
essentially the same after the present epoch, reflecting the halting growth of
the Cosmic Web as Lambda gets to dominate the expansion of the Universe. The
same trend can be seen in the stagnation of the development of the mass
function of virialized haloes and bound objects. The situation is considerably
different when looking at the internal evolution, quantified in terms of their
shape, compactness and density profile, and substructure in terms of their
multiplicity function. We find a continuing evolution from a wide range of
triaxial shapes at a = 1 to almost perfect spherical shapes at a = 100. We also
find a systematic trend towards a higher concentration. Meanwhile, we see their
substructure gradually disappearing, as the surrounding subclumps fall in and
merge to form one coherent, virialized system.
