2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209369Let $D$ be an integral domain and $\star$ a semistar operation stable and of finite type on it. In this paper, we are concerned with the study of the semistar (Krull) dimension theory of polynomial rings over $D$. We introduce and investigate the notions of $\star$-universally catenarian and $\star$-stably strong S-domains and prove that, every $\star$-locally finite dimensional Prüfer $\star$-multiplication domain is $\star$-universally catenarian, and this implies $\star$-stably strong S-domain. We also give new characterizations of $\star$-quasi-Prüfer domains introduced recently by Chang and Fontana, in terms of these notions.Accepted in communications in algebraCommutative Algebra13G05, 13B24, 13A15, 13C15text