  The notion of 'slope rational connectedness' is introduced in the context of
smooth orbifold pairs. The main result parallels the characterization of the
rational connectedness of projective manifolds in terms of either the
non-existence of holomorphic covariant tensors, or of absence of fibrations
onto manifolds with pseudo-effective canonical bundle, or of existence of
movable classes for which the minimal slope of the tangent bundle is positive.
We then use this result to construct the `rational quotient map' in orbifold
category.
