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We want to understand global observable consequences of different physicalprocesses and initial properties on the demographics of the planetarypopulation. We use the Generation III Bern model to perform planetarypopulation synthesis. We synthesise five populations with each a differentinitial number of Moon-mass embryos per disc: 1, 10, 20, 50, and 100. The lastis our nominal population around 1 Sun-mass stars. The properties of giantplanets do not change much as long as there are at least 10 embryos in eachsystem. The study of giants can thus be done with simulations requiring lesscomputational resources. For inner terrestrial planets, only the 100-embryospopulation is able to attain the giant-impact stage. In that population, eachplanetary system contains on average 8 planets more massive than 1 $M_\oplus$.The fraction of systems with giants planets at all orbital distances is 18%,but only 1.6% are at > 10 au. Systems with giants contain on average 1.6 suchplanets. The frequency of terrestrial and super-Earth planets peaks at astellar [Fe/H] of -0.2 and 0.0, respectively, being limited at lower [Fe/H] bya lack of building blocks, and by (for them) detrimental growth of more massivedynamically active planets at higher [Fe/H]. The frequency of more massiveplanets (Neptunian, giants) increases monotonically with [Fe/H]. The fastmigration of planets in the 5-50 $M_\oplus$ range is reduced by the presence ofmultiple lower-mass inner planets in the multi-embryos populations. We presentone of the most comprehensive simulations of (exo)planetary system formationand evolution to date. For theory, they provide the framework toobservationally test the global statistical consequences of theoretical modelsfor specific physical processes. This is a important ingredient towards thedevelopment of a standard model of planetary formation and evolution.

The New Generation Planetary Population Synthesis (NGPPS). II. Planetary population of solar-like stars and overview of statistical results