This paper offers a minimalist account of the distribution of the features of case, number and gender in Polish phrases with cardinal numerals and vague quantifiers (Q-NPs) in the presence and absence of genitive of quantification (GQ) based on the assumption that GQ-cardinal numerals and vague quantifiers are phrasal and are merged as adjuncts to the projection of a null functional head (F), a phase head that values its complement with GQ in contexts in which GQ is not overridden by inherent theta-related or lexical case. Whether the null head F inserted in the derivation has unvalued features of number and gender has consequences for the syntactic computation of agreement relations, in which features may be shared. Heterogeneous case dist...