The aim of the paper is to give a semantic description of the independent or bare partitive genitive (IPG) in Lithuanian in rather neutral, functional terms. The IPG is a multi-faceted category that bears on the domains of quantification and (in)definiteness. On its quantificational reading, the IPG encodes an implicit quantifier, arbitrary in its value. I have used the notion of (un)boundedness (re-)introduced in Paul Kiparsky’s (1998) seminal paper on the partitive case in Finnish. NP-internally, the IPG has two main readings: unbounded and bounded reading. The first reading provides the concept of the participant rather than ‘zooming in’ on particular instantiations. It is extremely weak referentially, probably the weakest option available in Lithuanian. This reading is restricted to those verbs in Lithuanian that allow their arguments to be kind-referring NPs (e.g., the subject of the existential to be, or object of to know). On the bounded reading, in turn, the IPG encodes an undetermined but delimited set, the reading is existential and resembles indefinite plurals. The individuals introduced by this reading are stored in the discourse model and may be picked up by anaphoric pronouns in the following discourse. They never constitute primary or foregrounded information of the message, though. Furthermore, I have claimed that the incremental-theme verbs and verbs of transfer in East Lithuanian interact with the IPG-marked object with respect to their aspectual properties. Here only the bounded reading of the IPG is available. This explains the ban on the occurrence of IPG in imperfective contexts in Lithuanian (such as progressive, which has no grammatical marking in Lithuanian, generic and iterated atelics) with incremental-theme verbs, because the imperfective interpretation induces an inherently unbounded event which is not compatible with the bounded reading of the IPG. Both bounded and unbounded values are assumed to be originally two different readings of the same implicit quantifier that have, however, acquired different distributions in the course of time.