  We consider particles in three-dimensional space, which have a certain
probability to find themselves in a thin layer (``plane''), where they are
assumed to be well described by a planar Hamiltonian and are subject to
Aharonov-Bohm-type interaction. We demonstrate that their planar motion is then
anyonlike, with the ``effective statistical parameter'' proportional
essentially to the square of the probability. We also show that charge-flux
composites with solenoids of finite length, provided they are themselves
fermions, can form a bound state in which they behave like anyons, without any
external potential confining them to a plane.
