  According to the latest evidence, the Universe is entering an era of
exponential expansion, where gravitationally bound structures will get
disconnected from each other, forming isolated `island universes'. In this
scenario, we present a theoretical criterion to determine the boundaries of
gravitationally bound structures and a physically motivated definition of
superclusters as the largest bound structures in the Universe. We use the
spherical collapse model self-consistently to obtain an analytical condition
for the mean density enclosed by the last bound shell of the structure (2.36
times the critical density in the present Universe, assumed to be flat, with 30
per cent matter and 70 per cent cosmological constant, in agreement with the
previous, numerical result of Chiueh and He). $N$-body simulations extended to
the future show that this criterion, applied at the present cosmological epoch,
defines a sphere that encloses $\approx 99.7$ per cent of the particles that
will remain bound to the structure at least until the scale parameter of the
Universe is 100 times its present value. On the other hand, $(28\pm 13)$ per
cent of the enclosed particles are in fact not bound, so the enclosed mass
overestimates the bound mass, in contrast with the previous, less rigorous
criterion of, e.~g., Busha and collaborators, which gave a more precise mass
estimate. We also verify that the spherical collapse model estimate for the
radial infall velocity of a shell enclosing a given mean density gives an
accurate prediction for the velocity profile of infalling particles, down to
very near the centre of the virialized core.
