I always heard and read the expression "status quo" but I just found the alternative spelling "statu quo" in the Italian translation of Motivational Interviewing by Miller e Rollnick.
Which is more correct?
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Status quō literally means "the state in which [things currently are]". It's normally used as a noun, as in "maintaining the status quo".
Statū quō literally means "[in] the state in which [things currently are]". I've only seen this form used as an adverb or adjective, usually preceded by in; cmw quotes the OED quoting Watson from 1602:
The seculars are but in statu quo prius, and cannot be in a worse then they are in at this present.
That is, the seculars are in the same state as before. But I wouldn't use this form as a noun on its own; I wouldn't talk about *preserving the statu quo, for example.
However, I wouldn't generally expect correct Latin case marking in other languages. It might be pedantically correct to talk about "preserving the statum quo", "referring to the statui quo", or "compared to the statu quo"—but English (and Italian) don't do this sort of case marking on nouns; it's simply not part of their grammar. So I wouldn't be surprised to see either of these forms generalized to all situations, like how we don't talk about planting a cactum (or multiple cactos) or going to the circui.