  We study a confined mixture of bosons and fermions in the quantal degeneracy
regime with attractive boson-fermion interaction. We discuss the effect that
the presence of vortical states and the displacement of the trapping potentials
may have on mixtures near collapse, and investigate the phase stability diagram
of the K-Rb mixture in the mean field approximation supposing in one case that
the trapping potentials felt by bosons and fermions are shifted from each
other, as it happens in the presence of a gravitational sag, and in another
case, assuming that the Bose condensate sustains a vortex state. In both cases,
we have obtained an analytical expression for the fermion effective potential
when the Bose condensate is in the Thomas-Fermi regime, that can be used to
determine the maxima of the fermionic density. We have numerically checked that
the values one obtains for the location of these maxima using the analytical
formulas remain valid up to the critical boson and fermion numbers, above which
the mixture collapses.
