Efficient magnetic braking is a formidable obstacle to the formation of rotationally supported disks (RSDs) around protostars in magnetized dense cores. We have previously shown, through 2D (axisymmetric) non-ideal MHD simulations, that removing very small grains (VSGs: ~10 AA$~$to few 100 AA) can greatly enhance ambipolar diffusion and enable the formation of RSDs. Here we extend the simulations of disk formation enabled by VSG removal to 3D. We find that the key to this scenario of disk formation is that the drift velocity of the magnetic field almost cancels out the infall velocity of the neutrals in the $10^2$-$10^3$ AU-scale pseudo-disk where the field lines are most severely pinched and most of protostellar envelope mass infall occurs. As a result, the bulk neutral envelope matter can collapse without dragging much magnetic flux into the disk-forming region, which lowers the magnetic braking efficiency. We find that the initial disks enabled by VSG removal tend to be Toomre-unstable, which leads to the formation of prominent spiral structures that function as centrifugal barriers. The piling-up of infall material near the centrifugal barrier often produces dense fragments of tens of Jupiter masses, especially in cores that are not too strongly magnetized. Some fragments accrete onto the central stellar object, producing bursts in mass accretion rate. Others are longer lived, although whether they can survive long-term to produce multiple systems remains to be ascertained. Our results highlight the importance of dust grain evolution in determining the formation and properties of protostellar disks and potentially multiple systems.
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