  Planes of satellites are observed around many galaxies. However, these
observations are still considered a point of tension for the $\Lambda$CDM
paradigm. We use the fully hydrodynamical cosmological $\Lambda$CDM
state-of-the-art simulation Magneticum Pathfinder to investigate the existence
of such planes over a large range of haloes, from Milky Way to galaxy cluster
masses. To this end, we develop the Momentum in Thinnest Plane (MTP) method to
identify planes and quantify the properties of their constituent satellites,
considering both position and momentum. We find that thin planes ($20\%\cdot
R_\mathrm{halo}$) containing at least $50\%$ of the total number of satellites
can be found in almost all systems. In Milky Way mass-like systems, around 86\%
of such planes are even aligned in momentum ($90\%$ of the total satellite
momentum), where the fraction is smaller if more satellites are required to be
inside the plane. We further find a mass dependency, with more massive systems
exhibiting systematically thicker planes. This may point towards the change
from continuous accretion of small objects along filaments and sheets for less
massive haloes to the accretion of large objects (e.g., major mergers)
dominating the growth of more massive haloes. There is no correlation between
the existence of a plane and the main galaxy's morphology. Finally, we find a
clear preference for the minor axes of the satellite planes and the host galaxy
to be aligned, in agreement with recent observations.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics