  The core accretion mechanism is presently the most widely accepted cause of
the formation of giant planets. For simplicity, most models presently assume
that the growth of planetary embryos occurs in isolation. We explore how the
simultaneous growth of two embryos at the present locations of Jupiter and
Saturn affects the outcome of planetary formation. We model planet formation on
the basis of the core accretion scenario and include several key physical
ingredients. We consider a protoplanetary gas disk that exponentially decays
with time. For planetesimals, we allow for a distribution of sizes from 100~m
to 100~km with most of the mass in the smaller objects. We include planetesimal
migration as well as different profiles for the surface density $\Sigma$ of the
disk. The core growth is computed in the framework of the oligarchic growth
regime and includes the viscous enhancement of the planetesimal capture
cross-section. Planet migration is ignored. By comparing calculations assuming
formation of embryos in isolation to calculations with simultaneous embryo
growth, we find that the growth of one embryo generally significantly affects
the other. This occurs in spite of the feeding zones of each planet never
overlapping. The results may be classified as a function of the gas surface
density profile $\Sigma$: if $\Sigma \propto r^{-3/2}$ and the protoplanetary
disk is rather massive, Jupiter's formation inhibits the growth of Saturn. If
$\Sigma \propto r^{-1}$ isolated and simultaneous formation lead to very
similar outcomes; in the the case of $\Sigma \propto r^{-1/2}$ Saturn grows
faster and induces a density wave that later acclerates the formation of
Jupiter. Our results indicate that the simultaneous growth of several embryos
impacts the final outcome and should be taken into account by planet formation
models.
