  We introduce a new class of growth models, with a surface restructuring
mechanism in which impinging particles may dislodge suspended particles,
previously aggregated on the same column in the deposit. The flux of these
particles is controlled through a probability $p$. These systems present a
crossover, for small values of $p$, from random to correlated (KPZ) growth of
surface roughness, which is studied through scaling arguments and Monte Carlo
simulations on one- and two-dimensional substrates. We show that the crossover
characteristic time $t_{\times}$ scales with $p$ according to $t_{\times}\sim
p^{-y}$ with $y=(n+1)$ and that the interface width at saturation $W_{sat}$
scales as $W_{sat}\sim p^{-\delta}$ with $\delta = (n+1)/2$, where $n$ is
either the maximal number of broken bonds or of dislodged suspended particles.
This result shows that the sets of exponents $y=1$ and $\delta=1/2$ or $y=2$
and $\delta=1$ found in all previous works focusing on systems with this same
type of crossover are not universal. Using scaling arguments, we show that the
bulk porosity $P$ of the deposits scales as $P\sim p^{y-\delta}$ for small
values of $p$. This general scaling relation is confirmed by our numerical
simulations and explains previous results present in literature.
