We study limiting properties of ratios of ordered points of point processes whose
intensity measures have regularly varying tails, giving a systematic treatment which
points the way to "large-trimming" properties of extremal processes and a variety
of applications. Our point process approach facilitates a connection with the negative
binomial process of Gregoire (1984) and consequently to certain generalised versions
of the Poisson-Dirichlet distribution. (C) 2018 Elsevier B.V. All rights reserved.