  Let G be a finite subgroup of GL_n(C). A study is made of the ways in which
resolutions of the quotient space C^n / G can parametrise G-constellations,
that is, G-regular finite length sheaves. These generalise G-clusters, which
are used in the McKay correspondence to construct resolutions of orbifold
singularities.
  A complete classification theorem is achieved, in which all the natural
families of G-constellations are shown to correspond to certain finite sets of
G-Weil divisors, which are a special sort of rational Weil divisor, introduced
in this paper. Moreover, it is shown that the number of equivalence classes of
such families is always finite.
  Explicit examples are computed throughout using toric geometry.
