  We study several one dimensional step flow models. Numerical simulations show
that the slope of the profile exhibits scaling in all cases. We apply a scaling
ansatz to the various step flow models and investigate their long time
evolution. This evolution is described in terms of a continuous step density
function, which scales in time according to D(x,t)=F(xt^{-1/\gamma}). The value
of the scaling exponent \gamma depends on the mass transport mechanism. When
steps exchange atoms with a global reservoir the value of \gamma is 2. On the
other hand, when the steps can only exchange atoms with neighboring terraces,
\gamma=4. We compute the step density scaling function for three different
profiles for both global and local exchange mechanisms. The computed density
functions coincide with simulations of the discrete systems. These results are
compared to those given by the continuum approach of Mullins.
