  To construct continuum stochastic growth equations for competitive
nonequilibrium surface-growth processes of the type RD+X that mixes random
deposition (RD) with a correlated-growth process X, we use a simplex
decomposition of the height field. A distinction between growth processes X
that do and do not create voids in the bulk leads to the definition of the {\it
effective probability} $p_{\mathrm{eff}}$ of the process X that is a measurable
property of the bulk morphology and depends on the {\it activation probability}
$p$ of X in the competitive process RD+X. The bulk morphology is reflected in
the surface roughening via {\it nonuniversal} prefactors in the universal
scaling of the surface width that scales in $p_{\mathrm{eff}}$. The equation
and the resulting scaling are derived for X in either a Kardar-Parisi-Zhang or
Edwards-Wilkinson universality class in $(1+1)$ dimensions, and illustrated by
an example of X being a ballistic deposition. We obtain full data collapse on
its corresponding universal scaling function for all $p \in (0;1]$. We outline
the generalizations to $(1+n)$ dimensions and to many-component competitive
growth processes.
