This paper explores variations on and connections between the topics mentioned in its title, using as something of an anchor the discussion in Valentin Goranko and Antti Kuusisto’s “Logics for propositional determinacy and independence”, a venture into what the authors call the logic of determinacy, which they contrast with (a demodalized version of) Jouko Väänänen’s modal dependence logic. As they make clear in their discussion, these logics are closely connected with the topics of noncontingency and supervenience. Two opening sections of the present paper address some of these connections, including related earlier logical work by the present author as well as very recent work by Jie Fan. The Väänänen-inspired treatment is presented in a third section, and then, in Sections 4 and 5, as a kind of centerpiece for the discussion, we follow Goranko and Kuusisto in elaborating one principal reason offered for preferring their own approach over that treatment, which concerns some anomalies over the behaviour of disjunction in the latter treatment. Sections 6 and 7 look at dependence and (several different versions of) disjunction in inquisitive logic, especially as presented by Ivano Ciardelli. Section 8 revisits the less formal property-supervenience literature with issues from the first two sections of the paper in mind, and we conclude with a Postscript addressing a further conceptual issue pertaining to the relation between modal and quantificational dependence logics.