  We analyze in detail the Solid-On-Solid model (SOS) for growth processes on a
square substrate in 2+1 dimensions. By using the Markovian surface properties,
we introduce an alternative approach for determining the roughness exponent of
a special type of SOS model-the Restricted-Solid-On-Solid model (RSOS)- in 2+1
dimensions. This model is the SOS model with the additional restriction that
the height difference must be S=1. Our numerical results show that the
behaviour of the SOS model in 2+1 dimensions for approximately $S\geq
S_{\times}\sim 8$ belongs to the two different universality classes: during the
initial time stage, $t< t_{\times}$ it belongs to the Random-Deposition (RD)
class, while for $t_{\times}<t\ll t_{sat}$ it belongs to the
Kardar-Parisi-Zhang (KPZ) universality class. The crossover time ($t_{\times}$)
is related to S via a power law with exponent, $\eta=1.99\pm0.02$ at $1\sigma$
confidence level which is the same as that for 1+1 dimensions reported in Ref.
\cite{e1}. Using the structure function, we compute the roughness exponent. In
contrast to the growth exponent, the roughness exponent does not show crossover
for different values of S. The scaling exponents of the structure function for
fixed values of separation distance versus S in one and two space dimensions
are $\xi=0.92\pm0.05$ and $\xi=0.86\pm0.05$ at $1\sigma$ confidence level,
respectively.
