  This paper is concerned with the existence and stability of phase transition
steady states to a quasi-linear hyperbolic-parabolic system of chemotactic
aggregation, which was proposed in \cite{ambrosi2005review,
gamba2003percolation} to describe the coherent vascular network formation
observed {\it in vitro} experiment. Considering the system in the half line $
\mathbb{R}_{+}=(0,\infty)$ with Dirichlet boundary conditions, we first prove
the existence \textcolor{black}{and uniqueness of non-constant phase transition
steady states} under some structure conditions on the pressure function. Then
we prove that this unique phase transition steady state is nonlinearly
asymptotically stable against a small perturbation. We prove our results by the
method of energy estimates, the technique of {\it a priori} assumption and a
weighted Hardy-type inequality.
