  Aims. In the context of the core instability model, we present calculations
of in situ giant planet formation. The oligarchic growth regime of solid
protoplanets is the model adopted for the growth of the core. Methods. The full
differential equations of giant planet formation were numerically solved with
an adaptation of a Henyey-type code. The planetesimals accretion rate was
coupled in a self-consistent way to the envelope's evolution. Results. We
performed several simulations for the formation of a Jupiter-like object by
assuming various surface densities for the protoplanetary disc and two
different sizes for the accreted planetesimals. We find that the atmospheric
gas drag gives rise to a major enhancement on the effective capture radius of
the protoplanet, thus leading to an average timescale reduction of 30% -- 55%
and ultimately to an increase by a factor of 2 of the final mass of solids
accreted as compared to the situation in which drag effects are neglected. With
regard to the size of accreted planetesimals, we find that for a swarm of
planetesimals having a radius of 10 km, the formation time is a factor 2 to 3
shorter than that of planetesimals of 100 km, the factor depending on the
surface density of the nebula. Moreover, planetesimal size does not seem to
have a significant impact on the final mass of the core.
