  We show that certain types of the three-legged accessibility property of a
partially hyperbolic diffeomorphism imply the existence of a unique minimal set
for one strong foliation and the transitivity of the other one. In case the
center dimension is one, we also give a criteria to obtain three-legged
accessibility in a robust way. We show some applications of our results to the
time-one map of Anosov flows, skew products and certain Anosov diffeomorphisms
with partially hyperbolic splitting.
