  The structure of planetary systems around their host stars depends on their
initial formation conditions. Massive planets will likely be formed as a
consequence of rapid migration of planetesimals and low mass cores into
specific trapping sites in protoplanetary discs. We present analytical modeling
of inhomogeneities in protoplanetary discs around a variety of young stars, -
from Herbig Ae/Be to classical T Tauri and down to M stars, - and show how they
give rise to planet traps. The positions of these traps define the initial
orbital distribution of multiple protoplanets. We investigate both corotation
and Lindblad torques, and show that a new trap arises from the
(entropy-related) corotation torque. This arises at that disc radius where disc
heating changes from viscous to stellar irradiation dominated processes. We
demonstrate that up to three traps (heat transitions, ice lines and dead zones)
can exist in a single disc, and that they move differently as the disc
accretion rate $\dot{M}$ decreases with time. The interaction between the giant
planets which grow in such traps may be a crucial ingredient for establishing
planetary systems. We also demonstrate that the position of planet traps
strongly depends on stellar masses and disc accretion rates. This indicates
that host stars establish preferred scales of planetary systems formed around
them. We discuss the potential of planet traps induced by ice lines of various
molecules such as water and CO, and estimate the maximum and minimum mass of
planets which undergo type I migration. We finally apply our analyses to
accounting for the initial conditions proposed in the Nice model for the origin
of our Solar system.
