I speculated that the chosen object that he elevated to art status was so common that they could still somehow be found in men's rooms of antique vintage. But it seemed ridiculous, even in the light of Duchamp's statement that plumbing was one of America's contributions to the world of art (or something like that).
This article -- illustrated by the photo at right of the original and a reproduction -- has the answer:
“Fountain” was not a coveted art object until well after the second world war, when Duchamp became a cult figure among Pop artists. In response to the art world's desire to see his legendary lavatory, Duchamp authorised curators to purchase urinals in his name in 1950, 1953 and 1963. ... Then in 1964, in association with Arturo Schwarz, a Milan art dealer, historian and collector, the artist made the momentous decision to issue 12 replicas (an edition of eight with four proofs) of his most important ready-mades, including the urinal. ... One of the many ironies of the Schwarz urinals is that they are carefully crafted earthenware sculptures modelled on the Stieglitz photo of the “original”.The article continues with a discussion of the locations and the mysterious appearances of other signed and unsigned urinal replicas that may or may not be authentic Duchamp remade readymades. Needless to say the concept of authenticity is elusive in this discussion. No surprise: Andy Warhol played a role. All the usual dada antics resurface as I love them to do. The article concludes:
Duchamp's relationship to commerce was not naive. Although he preferred to give away his work rather than sell it, he made a living as an art dealer for many years. Duchamp was also an able chess player who could think a good few moves ahead. One wonders whether the Dada master, who challenged the notion of the authentic artwork, might not be amused by the way these questionable “Fountains” muddy the waters of his current market. “My production,” he once said, “has no right to be speculated upon.”Duchamp set up the art world and keeps playing tricks long after his death. What a pleasure for a lover of dada. Almost better than his most famous remade readymade, Mona Lisa with a drawn-on mustache. For more see Marcel Duchamp is Relevant.