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The formation and evolution of protoplanetary discs remains a challenge fromboth a theoretical and numerical standpoint. In this work we first perform aseries of tests of our new hybrid algorithm presented in Glaschke, Amaro-Seoaneand Spurzem 2011 (henceforth Paper I) that combines the advantages of highaccuracy of direct-summation N-body methods with a statistical description forthe planetesimal disc based on Fokker-Planck techniques. We then address theformation of planets, with a focus on the formation of protoplanets out ofplanetesimals. We find that the evolution of the system is driven by encountersas well as direct collisions and requires a careful modelling of the evolutionof the velocity dispersion and the size distribution over a large range ofsizes. The simulations show no termination of the protoplanetary accretion dueto gap formation, since the distribution of the planetesimals is only subjectedto small fluctuations. We also show that these features are weakly correlatedwith the positions of the protoplanets. The exploration of different impactstrengths indicates that fragmentation mainly controls the overall mass loss,which is less pronounced during the early runaway growth. We prove that thefragmentation in combination with the effective removal of collisionalfragments by gas drag sets an universal upper limit of the protoplanetary massas a function of the distance to the host star, which we refer to as the millcondition.

Hybrid methods in planetesimal dynamics: Formation of protoplanetary systems and the mill condition