  Starting from the most general harmonic superspace action of self-interacting
Q^+ hypermultiplets in the background of N=2 conformal supergravity, we derive
the general action for the bosonic sigma model with a generic 4n dimensional
quaternionic-Kahler (QK) manifold as the target space. The action is determined
by the analytic harmonic QK potential. We find out this action to have two flat
limits. One gives the hyper-Kahler sigma model with a 4n dimensional target
manifold, while another yields a conformally invariant sigma model with 4(n+1)
dimensional hyper-Kahler target. We work out the harmonic superspace version of
the QK quotient construction and use it to give a new derivation of QK
extensions of Taub-NUT and Eguchi-Hanson metrics. We analyze in detail the
geometrical and symmetry structure of the second metric. The QK sigma model
approach allows us to reveal the enhancement of its isometry group to SU(3) or
SU(2,1) at the special relations between its parameters : the Einstein constant
and the "mass".
