  In this paper, we study quotients of groupoids and coarse moduli spaces of
stacks in a general setting. Geometric quotients are not always categorical,
but we present a natural topological condition under which a geometric quotient
is categorical. We also show the existence of geometric quotients of finite
flat groupoids and give explicit local descriptions. Exploiting similar
methods, we give an easy proof of the existence of quotients of flat groupoids
with finite stabilizers. As the proofs do not use noetherian methods and are
valid for general algebraic spaces and algebraic stacks, we obtain a slightly
improved version of Keel and Mori's theorem.
