Zappa-Szép product groupoids and C*-blends

We study the external and internal Zappa-Szép product of topological groupoids.We show that under natural continuity assumptions the Zappa-Szép product groupoid is étale if and only if the individual groupoids are étale. In our main result we show that the C*-algebra of a locally compact Hausdorff étale Zappa-Szép product groupoid is a C*-blend, in the sense of Exel, of the individual groupoid C*-algebras. We finish with some examples, including groupoids built from ⁎-commuting endomorphisms, and skew product groupoids.