  We derive self similar solutions for ultra-relativistic shock waves
propagating into cold material of powerlaw density profile in radius rho ~
r^-k. We treat both implosions and explosions in three geometries: planar,
cylindrical and spherical. For spherical explosions these are the first type
solutions of Blandford and McKee for k<4 and the second type solutions found by
Best and Sari for k>5-sqrt(3/4). In addition we find new, hollow (with
evacuated interior), first type solutions that may be applicable for 4<k<17/4.
This ``sequence'' with increasing k of first type solutions, hollow first type
solutions, and then second type solutions is reminiscent of the
non-relativistic sequence. However, while in the non relativistic case there is
a range of k which corresponds to a ``gap'' - a range in $k$ with neither first
nor second type solutions which separates the hollow first type solutions and
the second type solutions, here there is an ``overlap'': a range of k for which
current considerations allow for both hollow first and second type solutions.
Further understanding is needed to determine which of the two solutions apply
in this overlap regime. We provide similar exploration for the other geometries
and for imploding configurations. Interestingly, we find a gap for imploding
spherical shocks and exploding planar shocks and an overlap for imploding
planar solutions. Cylindrical configurations have no hollow solutions and
exhibit direct transition from first type to second type solutions, without a
gap or an overlap region.
