  We introduce the notions of h-conformal slant submersions and almost
h-conformal slant submersions from almost quaternionic Hermitian manifolds onto
Riemannian manifolds as a generalization of Riemannian submersions,
horizontally conformal submersions, slant submersions, h-slant submersions,
almost h-slant submersion and conformal slant submersions.
  We investigate several properties of these including the integrability of
distributions, the geometry of foliations and the conditions for such maps to
be totally geodesic. Further we give some examples of such maps.
