Universality in static spherically symmetric solutions of f(R) gravity

f(R) gravity is a well-known modification of General Relativity, that can be reduced to a scalar-tensor theory by a conformal transformation (Einstein frame). We study static spherically symmetric (SSS) asymptotically flat vacuum configurations of the f(R) gravity in the Einstein frame for three known scalaron potentials. The main attention is paid to solutions in case of astrophysically relevant configuration masses and scalaron mass $\mu$ larger than several meV. Analytical and numerical analysis reveals remarkably similar properties of some elements of the SSS solutions for different M, $\mu$ and sizes of the scalarization region $r_0$. In particular, the scalaron field has universal behavior regardless of the configurations mass and $r_0>100 r_g$ in case of each of the models considered. Moreover, some elements of the solutions are practically the same for the different models. Asymptotic parameters of the metric near the naked singularity at the center of the SSS configuration are obtained for all the models.