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Aims. The connection between initial disc conditions and final orbital andphysical properties of planets is not well-understood. In this paper, wenumerically study the formation of planetary systems via pebble accretion andinvestigate the effects of disc properties such as masses, dissipationtimescales, and metallicities on planet formation outcomes. Methods. Weimproved the N-body code SyMBA that was modified by taking account of newplanet-disc interaction models and type II migration. We adopted the 'two-alphadisc' model to mimic the effects of both the standard disc turbulence and themass accretion driven by the magnetic disc wind. Results. We successfullyreproduced the overall distribution trends of semi-major axes, eccentricities,and planetary masses of extrasolar giant planets. We find that, when planetformation happens fast enough, giant planets are fully grown (Jupiter mass orhigher) and are distributed widely across the disc. On the other hand, whenplanet formation is limited by the disc's dissipation, discs generally formlow-mass cold Jupiters (CJs). Our simulations also naturally explain why hotJupiters (HJs) tend to be alone and how the observed eccentricity-metallicitytrends arise. The low-metallicity discs tend to form nearly circular andcoplanar HJs in situ, because planet formation is slower than high-metallicitydiscs, and thus protoplanetary cores migrate significantly before gasaccretion. The high-metallicity discs, on the other hand, generate HJs in situor via tidal circularisation of eccentric orbits. Both pathways usually involvedynamical instabilities, and thus HJs tend to have broader eccentricity andinclination distributions. When giant planets with very wide orbits('super-cold Jupiters') are formed, we find that they often belong tometal-rich stars, have eccentric orbits, and tend to have (~80%) companionsinterior to their orbits.

N-body simulations of planet formation via pebble accretion II. How various giant planets form