  Isolated low-mass stars are formed, in the standard picture, from the
collapse of dense cores condensed out of strongly magnetized molecular clouds.
The dynamically collapsing inflow traps nearly half of the critical magnetic
flux needed for the core support and deposits it in a small region surrounding
the protostar. It has been argued previously that the deposited flux can slow
down the inflow, allowing matter to pile up and settle along field lines into a
magnetically supported, circumstellar disk. Here we show that the disk
typically contains $\sim 10%$ of the stellar mass, and that it could become
self-gravitating under plausible conditions during the rapidly accreting,
``Class 0'' phase of star formation. Subsequent fragmentation of the
self-gravitating, magnetically subcritical disk, driven by magnetic diffusion,
could produce fragments of substellar masses, which collapse to form brown
dwarfs and possibly massive planets. This scenario predicts substellar object
formation at distances of order 100 AU from the central star, although orbital
evolution is possible after formation. It may provide an explanation for the
small, but growing, number of brown dwarf companions found around nearby stars
by direct imaging. The relatively large formation distances make the substellar
companions vulnerable to dynamic ejection, particularly in binary (multiple)
systems and dense clusters. Those ejected may account for, at least in part,
the isolated brown dwarfs and perhaps free-floating planetary mass objects.
