  In order to explain the main characteristics of the observed population of
extrasolar planets and the giant planets in the Solar System, we need to get a
clear understanding of which are the initial conditions that allowed their
formation. To this end we develop a semi-analytical model for computing
planetary systems formation based on the core instability model for the gas
accretion of the embryos and the oligarchic growth regime for the accretion of
the solid cores. With this model we explore not only different initial discs
profiles motivated by similarity solutions for viscous accretion discs, but we
also consider different initial conditions to generate a variety of planetary
systems assuming a large range of discs masses and sizes according to the last
results in protoplanetary discs observations. We form a large population of
planetary systems in order to explore the effects in the formation of assuming
different discs and also the effects of type I and II regimes of planetary
migration, which were found to play fundamental role in reproducing the
distribution of observed exoplanets. Our results show that the observed
population of exoplanets and the giant planets in the Solar System are well
represented when considering a surface density profile with a power law in the
inner part characterized by an exponent of -1, which represents a softer
profile when compared with the case most similar to the MMSN model case.
