  We analyze theoretically the phase diagram of a triangular triple quantum dot
with strong onsite repulsion coupled to ferromagnetic leads. This model
includes the competition of magnetic ordering of local or itinerant magnetic
moments, geometric frustration and Kondo screening. We identify all the phases
resulting from this competition. We find that three Kondo phases -- the
conventional one, the two-stage underscreened one, and the one resulting from
the ferromagnetic Kondo effect -- can be realized at zero temperature, and all
are very susceptible to the proximity of ferromagnetic leads. In particular, we
find that the quantum dots are spin-polarized in each of these phases. Further,
we discuss the fate of the phases at non-zero temperatures, where a plethora of
competing energy scales gives rise to complex landscape of crossovers. Each
Kondo regime splits into a pair of phases, one not magnetized and one
comprising magnetically polarized quantum dots. We discuss our results in the
context of heavy-fermion physics in frustrated Kondo lattices.
