  We study here a standard next-nearest-neighbor (NNN) model of ballistic
growth on one- and two-dimensional substrates focusing our analysis on the
probability distribution function $P(M,L)$ of the number $M$ of maximal points
(i.e., local ``peaks'') of growing surfaces. Our analysis is based on two
central results: (i) the proof (presented here) of the fact that uniform
one--dimensional ballistic growth process in the steady state can be mapped
onto ''rise-and-descent'' sequences in the ensemble of random permutation
matrices; and (ii) the fact, established in Ref. \cite{ov}, that different
characteristics of ``rise-and-descent'' patterns in random permutations can be
interpreted in terms of a certain continuous--space Hammersley--type process.
For one--dimensional system we compute $P(M,L)$ exactly and also present
explicit results for the correlation function characterizing the enveloping
surface. For surfaces grown on 2d substrates, we pursue similar approach
considering the ensemble of permutation matrices with long--ranged
correlations. Determining exactly the first three cumulants of the
corresponding distribution function, we define it in the scaling limit using an
expansion in the Edgeworth series, and show that it converges to a Gaussian
function as $L \to \infty$.
