It is generally believed that the patterns of in-host migration of the infective stages of most invasive macroparasites of man and domestic animals are matters of established fact. In reality, the textbook treatment of this topic, and much of the experimental approach to it, are a legacy of an uncritical past. With few exceptions the true picture concerning particular host/parasite systems is confused by the acceptance of inadequate criteria of proof. In important instances these bogus ‘proofs’ have been generalized within a suspect inductive framework which employs the basic assumption that all migratory parasites that enter the same portal and travel to the same destination do so by the same route. The discussion of such issues serves as a background to the presentation in detail of a more rigorous conceptual and experimental framework.

In this paper we develop some results presented by Gani (2004), deriving moments for random allocation processes. These moments correspond to the allocation processes reaching some domain boundary. Exact formulae for means, variances, and probability generating functions as well as some asymptotic formulae for moments of random allocation processes are obtained. A special choice of the asymptotics and of the domain allows us to reduce a complicated numerical procedure to a simple asymptotic one.