  We study the Restricted Solid on Solid model for surface growth in spatial
dimension $d=2$ by means of a multi-surface coding technique that allows to
produce a large number of samples of samples in the stationary regime in a
reasonable computational time. Thanks to: (i) a careful finite-size scaling
analysis of the critical exponents, (ii) the accurate estimate of the first
three moments of the height fluctuations, we can quantify the wandering
exponent with unprecedented precision: $\chi_{d=2} = 0.3869(4)$. This figure is
incompatible with the long-standing conjecture due to Kim and Koesterlitz that
hypothesized $\chi_{d=2}=2/5$.
