We investigate the behavior of zeta functions of infinite graphs of groups which are quotients of cuspidal tree-lattices. This includes every non-uniform arithmetic quotient of the tree of $$extract_itex$$PGL_2$$/extract_itex$$ over local fields. Several examples of zeta functions are provided. In particular, we give pairs of non-isomorphic cuspidal tree-lattices which have the same Ihara zeta function and investigate the spectral behavior of a sequence of graphs of groups constructed in Efrat (1990) from a zeta function point of view. We will also discuss the case of complexes of groups arising as a standard arithmetic quotient of the building for $$extract_itex$$PGL_3$$/extract_itex$$.