On homomorphisms from a fixed representation to a general representation 
of a quiver

William Crawley-Boevey

Trans. Amer. Math. Soc. 348 (1996), pp. 1909-1919 

Abstract. We study the dimension of the space of homomorphisms from a
given representation X of a quiver to a general representation of dimension
vector \beta. We prove a theorem about this number, and derive two corollaries
concerning its asymptotic behaviour as \beta increases. These results are 
related to work of A. Schofield on homological epimorphisms from the path 
algebra to a simple artinian ring.