  We consider quantized vortices in two-component Bose-Einstein condensates and
three-component Fermi gases with attractive interactions. In these systems, the
vortex core can be either empty (normal in the fermion case) or filled with
another superfluid. We determine critical values of the parameters -- chemical
potentials, scattering lengths and, for Fermi gases, temperature -- at which a
phase transition between the two types of vortices occurs. Population imbalance
can lead to superfluid core (coreless) vorticity in multicomponent superfluids
which otherwise support only usual vortices. For multicomponent Fermi gases, we
construct the phase diagram including regions of coreless vorticity. We extend
our results to trapped bosons and fermions using an appropriate local
approximation, which goes beyond the usual Thomas-Fermi approximation for
trapped bosons.
