Push-out of Schemes

We study the existence of a push-out for two morphisms $Z \to X$ and $Z \to Y$ in the category of schemes. Push-out is a generalization of quotient of groupoid. We give a necessary and sufficient condition for the existence of a push-out in the flat projective case. We also give a sufficient condition for the existence of a push-out in the finite normal case, which does not assume any flatness. In particular, this gives a sufficient condition for the existence of a quotient of a finite groupoid on a normal scheme, which does not assume any flatness