In this paper we present a short review of statistical properties
of extrasolar planets, and of the core-accretion model and some of its
extensions. We also present results of population synthesis models
based on extended core-accretion planet formation models
(taking into account disk structure and evolution and migration
of the protoplanet, see Alibert et al. 2005a).
The population synthesis is carried out by calculating
the evolution of many disk-protoplanet
systems, assuming initial conditions (in particular
disk mass, disk lifetime and metallicity of the system)
taken from observations. Taking into account the
observational bias introduced by radial velocity surveys,
we statistically compare the results of our
models and the population of known extrasolar
planets. We show that our models are able to quantitatively reproduce the
mass and semimajor axes
of extrasolar planets around solar type
stars. Finally, we discuss the effect of the mass of the central star on the planet
formation process and on the final planetary population.