We present a set of numerical simulations addressing the effects of magnetic field strength and orientation on the flow-driven formation of molecular clouds. Fields perpendicular to the flows sweeping up the cloud can efficiently prevent the formation of massive clouds but permit the build-up of cold, diffuse filaments. Fields aligned with the flows lead to substantial clouds, whose degree of fragmentation and turbulence strongly depends on the background field strength. Adding a random field component leads to a selection effect for molecular cloud formation: high column densities are only reached at locations where the field component perpendicular to the flows is vanishing. Searching for signatures of colliding flows should focus on the diffuse, warm gas, since the cold gas phase making up the cloud will have lost the information about the original flow direction because the magnetic fields redistribute the kinetic energy of the inflows.
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