  We introduce the Mass Migration Process (MMP), a conservative particle system
on ${\mathbb N}^{{\mathbb Z}^d}$. It consists in jumps of $k$ particles ($k\ge
1$) between sites, with a jump rate depending only on the state of the system
at the departure and arrival sites of the jump. It generalizes misanthropes
processes, hence in particular zero range and target processes. After the
construction of MMP, our main focus is on its invariant measures. We obtain
necessary and sufficient conditions for the existence of translation-invariant
and invariant product probability measures. In the particular cases of
asymmetric mass migration zero range and mass migration target dynamics, these
conditions yield explicit solutions. If these processes are moreover
attractive, we obtain a full characterization of all translation-invariant,
invariant probability measures. We also consider attractiveness properties
(through couplings) and condensation phenomena for MMP. We illustrate our
results on many examples; in particular, we prove the coexistence of both
condensation and attractiveness in one of them.
