  We present numerical Monte Carlo results for the stationary state properties
of KPZ type growth in two dimensional surfaces, by evaluating the finite size
scaling (FSS) behaviour of the 2nd and 4th moments, $W_2$ and $W_4$, and the
skewness, $W_3$, in the Kim-Kosterlitz (KK) and BCSOS model. Our results agree
with the stationary state proposed by L\"assig. The roughness exponents
$W_n\sim L^{\alpha_n}$ obey power counting, $\alpha_n= n \alpha$, and the
amplitude ratio's of the moments are universal. They have the same values in
both models: $W_3/W_2^{1.5}= -0.27(1)$ and $W_4/W_2^{2}= +3.15(2)$. Unlike in
one dimension, the stationary state skewness is not tunable, but a universal
property of the stationary state distribution. The FSS corrections to scaling
in the KK model are weak and $\alpha$ converges well to the
Kim-Kosterlitz-L\"assig value $\alpha={2/5} $. The FSS corrections to scaling
in the BCSOS model are strong. Naive extrapolations yield an smaller value,
$\alpha\simeq 0.38(1)$, but are still consistent with $\alpha={2/5}$ if the
leading irrelevant corrections to FSS scaling exponent is of order
$y_{ir}\simeq -0.6(2)$.
