This paper proposes some new ideas about the semantics and syntax of the Japanese adnominal demonstratives a-no, ko-no and so-no. Semantically it is claimed that, while conveying familiarity by means of the demonstrative prefixes a-, ko- and so-, they lack uniqueness or maximality, and that the whole demonstrative phrase is existentially quantified; -no either marks partitivity (without excluding maximality) in the deictic and anaphoric uses, or-in bridging uses-serves to fill an argument slot (lexically encoded inside the following NP or created contextually). This analysis is supported by (i) the availability of sluicing, (ii) the distribution of numeral classifiers, and (iii) the similar behavior of French partitive constructions with respect to the "consistency test". Syntactically, Japanese adnominal demonstratives are analyzed as NP-adjuncts, an assumption supported by three morpho-syntactic properties: (i) The demonstrative prefixes, ko-, so-, a-systematically display the same morphology as that of the WH-prefix do-; (ii) The Japanese demonstratives may be preceded by a restrictive modifier, like other adjunct modifiers; (iii) They behave with respect to the ellipsis of the following NP as other no-marked expressions clearly identified as adnominal adjuncts. These hypotheses further shed light on some data from L2 acquisition.