  Considering some deposition models with limited mobility, we show that the
typical decay of the interface width to its saturation value is exponential,
which defines the crossover or saturation time \tau. We present a method to
calculate a characteristic time \tau_0 proportional to \tau and estimate the
dynamical exponent z. In one dimensional substrates of lengths L <~ 2048, the
method is applied to the Family model, the restricted solid-on-solid (RSOS)
model and the ballistic deposition. Effective exponents z_L converge to
asymptotic values consistent with the corresponding continuum theories. For the
two-dimensional Family model, the expected dynamic scaling hypothesis suggests
a particular definition of \tau_0 that leads to z=2, improving previous
calculations based on data collapse methods. For the two-dimensional RSOS
model, we obtain z ~ 1.6 and \alpha < 0.4, in agreement with recent large scale
simulations.
