  The theme of this article is the sampling of cluster and iterated cluster
point processes. It is partially a review, mainly of the Brix-Kendall exact
sampling method for cluster point processes and its adaptation by M{\o}ller and
Rasmussen to Hawkes branching point processes on the real line with light-tail
fertility rate are reviewed. The main novel aspect of this review is the
extension to non-Poissonian germ point processes. For this, a slight adaptation
is needed. A formal proof via Laplace transforms of the validity of the method
in terms of general clusters that are not necessarily point processes fits this
purpose and allows to include the exact sampling of Boolean models.
