  We give a classification of spherically symmetric kinematic self-similar
solutions. This classification is complementary to that given in a previous
work by the present authors [Prog. Theor. Phys. 108, 819 (2002)]. Dust
solutions of the second, zeroth and infinite kinds, perfect-fluid solutions and
vacuum solutions of the first kind are treated. The kinematic self-similarity
vector is either parallel or orthogonal to the fluid flow in the perfect-fluid
and vacuum cases, while the `tilted' case, i.e., neither parallel nor
orthogonal case, is also treated in the dust case. In the parallel case, there
are no dust solutions of the second (except when the self-similarity index
$\alpha$ is 3/2), zeroth and infinite kinds, and in the orthogonal case, there
are no dust solutions of the second and infinite kinds. Except in these cases,
the governing equations can be integrated to give exact solutions. It is found
that the dust solutions in the tilted case belong to a subclass of the Lema{\^
i}tre-Tolman-Bondi family of solutions for the marginally bound case. The flat
Friedmann-Robertson-Walker (FRW) solution is the only dust solution of the
second kind with $\alpha=3/2$ in the tilted and parallel cases and of the
zeroth kind in the orthogonal case. The flat, open and closed FRW solutions
with $p=-\mu/3$, where $p$ and $\mu$ are the pressure and energy density,
respectively, are the only perfect-fluid first-kind self-similar solutions in
the parallel case, while a new exact solution with $p=\mu$, which we call the
``singular stiff-fluid solution'', is the only such solution in the orthogonal
case. The Minkowski solution is the only vacuum first-kind self-similar
solution both in the parallel and orthogonal cases. Some important corrections
and complements to the authors' previous work are also presented.
