  We consider the motion of electrons confined to a two dimensional plane with
an externally applied perpendicular inhomogeneous magnetic field, both with and
without a Coulomb potential. We find that as long as the magnetic field is
slowly-decaying, bound states in magnetic quantum dots are indeed possible.
Several example cases of such magnetic quantum dots are considered in which one
can find the eigenvalues and eigenfunctions in closed form, including two
hitherto unknown quasi-exactly solvable models treated with confluent and
biconfluent Heun polynomials. It is shown how a modulation of the strength of
the magnetic field can exclude magnetic vortex-like states, rotating with a
certain angular momenta and possessing a definite spin orientation, from
forming. This indicates one may induce localization-delocalization transitions
and suggests a mechanism for spin-separation.
