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tokens: but it also reorganises the field topology, reducing the pinching of field lines close to the protostellar object, which also hinders the braking mechanism. Magnetic flux freezing and magnetic braking play a central role in the formation and development of the structures during the collapse. While in iMHD strongly amplified fields launch powerful magnetically supported outflows, these latter are much weaker or even disappear in niMHD. Misalignment between the initial rotation axis and the magnetic field direction does not appear to affect the niMHD results, showing that the physical flux dissipation due to ambipolar diffusion dominates the effects of initial configuration or numerical diffusion. For iMHD models, the additional mixing due to a tilted configuration also produces a diffusion plateau, similar to the ambipolar calculations. The disks that form in iMHD, characterised by strong magnetic support and an inflated shape (due to toroidal field lines loaded by infalling matter) strongly differ from the flat disks that form in niMHD. Formation and long-term evolution of disks in ideal MHD, however, are of dubious validity. Furthermore, the excessive magnetic braking generates unphysical counter-rotation inside the outflow or the magnetic tower. Interchange instabilities develop at the interface between the core and the disk, producing a redistribution of the flux and displacement of the core and disrupting the top-bottom symmetry in the system. Mesh resolution is found to strongly affect the simulation results in iMHD. None of these effects is observed in the niMHD simulations if the resolution is high enough. Disks with Keplerian velocity profiles around the protostar form in all our niMHD simulations for all different magnetisations and inclination angles. Their size and mass, however, is significantly reduced (by a factor ) in the more magnetised case () because of the increased braking. Such a magnetisation value seems to be typical of most molecular clouds. Aligned and misaligned initial configurations have no consequence on the disk properties in niMHD and yield disks with very similar properties. Magnetic flux diffusivity due to ambipolar diffusion thus appears to play a dominant role during the first protostellar collapse and the formation of the first Larson core and its surrounding disk, and it appears to dominate processes such as magnetic field and rotation axis orientations. Flux diffusion during the collapse allows the formation of quasi-Keplerian disks, solving the “disk formation crisis” found in ideal MHD. The mass, size, and magnetic properties (plasma ) of these disks, however, strongly depend on the initial magnetisation ( parameter) of the cloud, and in all cases the disks are significantly smaller and less massive than those found in pure hydrodynamics calculations. Characterisation of this plasma is of major importance to characterise viscous transport in disks, notably in the MRI. To complete our study, we will