Let $f:X\rightarrow Y$ be a morphism of schemes with smooth curves as fibers. Let $g:X\rightarrow Z$ be a family of smooth or nodal curves with $Z$ a regular scheme. Does the push-out $Z\coprod_X Y$ exist (at least as algebraic stack)? I saw existence of the push-out as algebraic space when one has $f$ a closed immersion and $g$ a finite morphism (fibers of dimension zero). I am wondering what is going on if the fibers have dimension one.