  This paper reports on the results of a numerical investigation designed to
address how the initially anisotropic appearance of a GRB remnant is modified
by the character of the circumburst medium and by the possible presence of an
accompanying supernova (SN). Axisymmetric hydrodynamical calculations of light,
impulsive jets propagating in both uniform and inhomogeneous external media are
presented, which show that the resulting dynamics of their remnants since the
onset of the non-relativistic phase is different from the standard self-similar
solutions. Because massive star progenitors are expected to have their close-in
surroundings modified by the progenitor winds, we consider both free winds and
shocked winds as possible external media for GRB remnant evolution. Abundant
confirmation is provided here of the important notion that the morphology and
visibility of GRB remnants are determined largely by their circumstellar
environments. For this reason, their detectability is highly biased in favor of
those with massive star progenitors; although, in this class of models, the
beamed component may be difficult to identify because the GRB ejecta is
eventually swept up by the accompanying SN. The number density of asymmetric
GRB remnants in the local Universe could be, however, far larger if they expand
in a tenuous interstellar medium, as expected for some short GRB progenitor
models. In these sources, the late size of the observable, asymmetric remnant
could extend over a wide, possibly resolvable angle and may be easier to
constrain directly.
