  The goal of this paper is to classify parametrically parabolic submanifolds
in any codimension. First, we describe the ones that are ruled and show that
they are the only parabolic submanifolds that admit an isometric immersion as a
hypersurface. Then, we classify the nonruled ones by two different means. In
fact, we provide the polar and bipolar parametrizations, each of which is
associated to a parabolic surface and a function on the surface which satisfies
a parabolic differential equation. To conclude, we describe the structure of
the singular set of the nonruled parabolic submanifolds.
