  We study the properties of a trapped interacting three component Fermi gas.
We assume that one of the components can have a different mass from the other
two. We calculate the different phases of the three component mixture and find
a rich variety of different phases corresponding to different pairing channels,
and simple ways of tuning the system from one phase to another. In particular,
we predict co-existence of several different superfluids in the trap, forming a
shell structure, and phase transitions from this mixture of superfluids to a
single superfluid when the system parameters or temperature is varied. Such
shell structures realize superfluids with a non-trivial spatial topology and
leave clear observable signatures in the density profile of the gas.
