  We show that for any quasimeromorphic mapping with an essential singularity
at infinity, there exist points whose iterates tend to infinity arbitrarily
slowly. This extends a result by Nicks for quasiregular mappings, and Rippon
and Stallard for transcendental meromorphic functions on the complex plane. We
further establish a new result for the growth rate of quasiregular mappings
near an essential singularity, and briefly extend some results regarding the
bounded orbit set and the bungee set to the quasimeromorphic setting.
