We examine the possibility of extending the class of copular constructions called specificational sentences (and to a lesser extent, of pseudo-cleft constructions) to transitive structures with avoir, as contextual variants. According to the way in which the under-specified noun is realised (prepositional or not), this verb presents two transitive variants of specificational constructions, the essential trait of which is to topicalise the base of the under-specified noun, which is inherent to the latter because of its syncategorematic nature.