  Any watershed, when defined on a stack on a normal pseudomanifold of
dimension d, is a pure (d -- 1)-subcomplex that satisfies a drop-of-water
principle. In this paper, we introduce Morse stacks, a class of functions that
are equivalent to discrete Morse functions. We show that the watershed of a
Morse stack on a normal pseudomanifold is uniquely defined, and can be obtained
with a linear-time algorithm relying on a sequence of collapses. Last, we prove
that such a watershed is the cut of the unique minimum spanning forest, rooted
in the minima of the Morse stack, of the facet graph of the pseudomanifold.
