  All $(-1)$-homogeneous axisymmetric no-swirl solutions of incompressible
stationary Navier-Stokes equations in three dimension which are smooth on the
unit sphere minus north and south poles have been classified in our earlier
work as a four dimensional surface with boundary. In this paper, we establish
near the no-swirl solution surface existence, non-existence and uniqueness
results on $(-1)$-homogeneous axisymmetric solutions with nonzero swirl which
are smooth on the unit sphere minus north and south poles.
