  In this paper we prove rigidity results for two-dimensional, closed,
immersed, non-necessarily convex, self-similar solutions of a wide class of
fully non-linear parabolic flows in $\mathbb{R}^3$. We show this self-similar
solutions are the round spheres centered at the origin provided it has genus
zero and satisfies a suitable upper pinching estimate for the Gaussian
curvature. As applications, we obtain rigidity results for the round sphere as
the only closed, immersed, genus zero, self-similar solution of several well
known flows, as the flow of the powers of mean curvature, the harmonic mean
curvature flow and the $\alpha$-Gaussian curvature flow for $\alpha\in(0,1/4)$.
We remark that our result does not assume any embeddedness condition.
