  We construct a large class of morphisms, which we call partial morphisms, of
groupoids that induce $*$-morphisms of maximal and minimal groupoid
$C^*$-algebras. We show that the association of a groupoid to its maximal
(minimal) groupoid $C^*$-algebra and the association of a partial morphism to
its induced morphism are functors (both of which extend the Gelfand functor).
We show how to geometrically visualize lots of $*$-morphisms between groupoid
$C^*$-algebras. As an application, we construct a groupoid models of the entire
inductive systems of the Jiang-Su algebra $\mathcal{Z}$ and the Razak-Jacelon
algebra $\mathcal{W}$.
