  Growth of interfaces during vapor deposition is analyzed on a discrete
lattice. It leads to finding distribution of local heights, measurable for any
lattice model. Invariance in the change of this distribution in time is used to
determine the finite size effects in various models The analysis is applied to
the discrete linear growth equation and Kardar-Parisi-Zhang (KPZ) equation.
  A new model is devised that shows early convergence to the KPZ dynamics.
  Various known conservative and non conservative models are tested on a one
dimensional substrate by comparing the growth results with the exact KPZ and
linear growth equation results. The comparison helps in establishing the
condition that helps in determining the presence of finite size effect for the
given model. The new model is used in 2+1 dimensions to predict close to the
true value of roughness constant for KPZ equation.
