  An open Riemann surface is called parabolic in case every bounded subharmonic
function on it reduces to a constant. Several authors introduced seemingly
different analogs of this notion for Stein manifolds of arbitrary dimension. In
the first part of this note we compile these notions of parabolicity and give
some immediate relations among them. In section 3 we relate some of these
notions to the linear topological type of the Fr\'echet space of analytic
functions on the given manifold. In sections 4 and 5 we look at some examples
and show, for example, that the complement of the zero set of a Weierstrass
polynomial possesses a continuous plurisubharmonic exhaustion function that is
maximal off a compact subset.
