  Bell's theorem shows that local measurements on entangled states give rise to
correlations incompatible with local hidden variable models. The degree of
quantum nonlocality is not maximal though, as there are even more nonlocal
theories beyond quantum theory still compatible with the nonsignalling
principle. In spite of decades of research, we still have a very fragmented
picture of the whole geometry of these different sets of correlations. Here we
employ both analytical and numerical tools to ameliorate that. First, we
identify two different classes of Bell scenarios where the nonsignalling
correlations can behave very differently: in one case, the correlations are
generically quantum and nonlocal while on the other quite the opposite happens
as the correlations are generically classical and local. Second, by randomly
sampling over nonsignalling correlations, we compute the distribution of a
nonlocality quantifier based on the trace distance to the local set. With that,
we conclude that the nonlocal correlations can show concentration phenomena:
their distribution is peaked at a distance from the local set that increases
both with the number of parts or measurements being performed.
