  In this work, we study the Neumann initial boundary value problem for a
three-component chemotaxis model in any dimensional bounded and smooth domains;
this model is used to describe the branching of capillary sprouts during
angiogenesis. First, we find three qualitatively simple sufficient conditions
for qualitative global boundedness, and then, we establish two types of global
stability for bounded solutions in qualitative ways. As a consequence of our
findings, the underlying system without chemotaxis and the effect of ECs
mitosis can not give rise to pattern formations. Our findings quantify and
extend significantly previous studies, which are set in lower dimensional
convex domains and are with no qualitative information.
