  With the high number of extrasolar planets discovered by now, it becomes
possible to constrain theoretical formation models in a statistical sense. This
paper is the first in a series in which we carry out a large number of planet
population synthesis calculations. We begin the series with a paper mainly
dedicated to the presentation of our approach, but also the discussion of a
representative synthetic planetary population of solar like stars. Based as
tightly as possible on observational data, we have derived probability
distributions for the most important initial conditions for the planetary
formation process. We then draw sets of initial conditions from these
distributions and obtain the corresponding synthetic planets with our formation
model. Although the main purpose of this paper is the description of our
methods, we present some key results: We find that the variation of the initial
conditions in the limits occurring in nature leads to the formation of planets
of large diversity. This formation process is best visualized in planetary
formation tracks, where different phases of concurrent growth and migration can
be identified. These phases lead to the emergence of sub-populations of planets
distinguishable in a mass-semimajor axis diagram. The most important ones are
the "failed cores", a vast group of core-dominated low mass planets, the
"horizontal branch", a sub-population of Neptune mass planets extending out to
6 AU, and the "main clump", a concentration of giant gaseous giants planets at
around 0.3-2 AU.
