  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.
