It is well known that for a Krull domain R, the divisor class group of R is a torsion group if and only if every subintersection of R is a ring of quotients. Thus a natural question is that under what conditions, for a non-Krull domain R, every (t-)subintersection (resp., t-linked overring) of R is a ring of quotients or every (t-)subintersection (resp., t-linked overring) of R is at. To address this question, we introduce the notions of *-compact packedness and *-coprime packedness of (an ideal of) an integral domain R for a star operation * of finite character, mainly t or w. We also investigate the t-theoretic analogues of related results in the literature.