  We analyse simulations of turbulent, magnetised molecular cloud cores
focussing on the formation of Class 0 stage protostellar discs and the physical
conditions in their surroundings. We show that for a wide range of initial
conditions Keplerian discs are formed in the Class 0 stage already.
Furthermore, we show that the accretion of mass and angular momentum in the
surroundings of protostellar discs occurs in a highly anisotropic manner, by
means of a few narrow accretion channels. The magnetic field structure in the
vicinity of the discs is highly disordered, revealing field reversals up to
distances of 1000 AU. These findings demonstrate that as soon as even mild
turbulent motions are included, the classical disc formation scenario of a
coherently rotating environment and a well-ordered magnetic field breaks down.
