  We develop a semi-analytical model for computing planetary system formation
with the aim of explaining the observed diversity of planetary systems
architectures and relate this primordial diversity with the initial properties
of the disc where they were born. We adopt different initial conditions based
on recent results in protoplanetary discs observations, to generate a variety
of planetary systems and analyze them statistically. We explore the relevance
of the mass and size of the disc, its metallicity, the mass of the central star
and the time-scale of gaseous disc dissipation, in defining the architecture of
the planetary system. We also test different values of some key parameters of
our model, to find out which factors best reproduce the diverse sample of
observed planetary systems. According to this, we predict which systems are the
most common in the solar neighbourhood. Our results show that planetary systems
with only terrestrial planets are the most common, being the only planetary
systems formed when considering low metallicity discs and which also represent
the best environment for the developing of rocky, potentially habitable
planets. We also found that planetary systems like our own are not rare in the
solar neighbourhood, being its formation favoured in massive discs where there
is not a large accumulation of solids in the inner region of the disc.
Regarding the planetary systems that harbor hot and warm Jupiter planets, we
found that this systems are born in very massive, metal-rich discs. Also a fast
migration rate is required in order to form these systems. According to our
results, most of the hot and warm Jupiter systems are composed by only one
giant planet, which is also a tendency of the current observational data.
