The focus of this paper is the possessive relation arising in several configurations between the complement of a locative preposition (u ‘at/by’ and k(o) ‘towards’ in Russian, bij ‘by’ in Dutch and la ‘to/at’ in Romanian, henceforth, u-preposition, heading a u-PP) and another NP in the same clause. I will show that u-PPs can introduce a number of distinct possessive relations in function of the syntactic context and that languages differ subtly in the matter of which such relations are available in which contexts. I will attribute this variation to the different semantic domains of these possessive PPs (locus-modifiers as opposed to event-modifiers) arising from the lexical specification of the possessive relators lexicalized by these prepositions.