  We construct axisymmetric self-similar solutions of transonic outflows
emanating from a point source including the effect of the rotation. The
solutions are constructed exclusively on the equatorial plane. The features of
solutions are determined by three parameters; the adiabatic index $\gamma$, the
dimensionless coordinate of the transonic point, and the dimensionless
azimuthal velocity at the transonic point. We classify the solutions into five
groups according to the asymptotic behaviors. We find that the behaviors of the
self-similar solutions change at $\gamma = 11/9$. In addition, some solutions
show double-power-law density profiles, which are usually seen in ejecta from a
binary merger or nova-like explosion. Thus, our self-similar solutions can be
applied not only to the outflow blowing from the central spinning objects, but
also to the ejecta erupted from the binary merger or nova-like explosion.
