The only one of its kind to survive
One fact frames the whole afterlife of this piece: it is the only assemblage of its kind by Hausmann to survive. He is not known to have made a series of these; the others, if there were others, are gone. So the Mechanical Head carries the weight of the idea more or less alone, which is part of why it is so reproduced and so fought over. Precisely: the only one of its kind to survive, not the only assemblage he ever made.
Its ownership chain, the provenance (the documented record of who has held a work of art, in order, from the maker to now), is short. On the Centre Pompidou’s own record, the piece passed to Hannah Höch, Hausmann’s partner and fellow Berlin Dadaist, around the time of their separation in 1922, and stayed in her keeping until 1966, when she returned it to him after repairs made for photography. Then, in 1974, three years after Hausmann’s death, the piece was bought by the Centre Pompidouin Paris (more precisely its Musée national d’art moderne), inventory number AM 1974-6, where it remains on view.
Public domain in the US, in copyright in Europe
A word on rights, because the two halves of the answer disagree and both are correct. The work was made and published around 1920, before 1930, which makes a faithful photograph of it public domain in the United States; that is the basis on which its image is freely shown. In Europe it is a different story: Hausmann died in 1971, so under the European term of the author’s life plus seventy years the work stays in copyright in the EU through 2041, and the museum asserts that claim there. The same object, free in one place and protected in another, depending only on the law you happen to be standing in.
A portrait of the spirit of the age
What Hausmann left is small enough to hold in two hands and large enough to have changed what sculpture could be. He took the most serious form in the whole tradition, the human head, and he refused to carve it, refused to ennoble it, refused to fill it. He built it from junk and left it empty, and he was right that the gesture would read. A century on, the blank wooden face with its cup and its ruler and its watch gear still says the thing he meant it to say about the rationalized, quantified, money-and-clock-ruled modern man: that his spirit is vacant, and what defines him is only the apparatus chance has glued to the outside of his skull.