  The purpose of this paper is to study the geometry of images of morphisms
from Mori dream spaces. First we prove that a variety which admits a surjective
morphism from a Mori dream space is again a Mori dream space. Secondly we
introduce a natural fan structure on the effective cone of Mori dream spaces.
We show that it encodes the information of Zariski decompositions, which in
turn is equivalent to the information of the variation of GIT quotients of
their Cox rings. Finally we show that under a surjective morphism between Mori
dream spaces, the fan of the target space coincides with the restriction of the
fan of the source.
