I know now days when a TV show or movie is made, most of the ships are designed as CGI models, so it's possible to produce an entire movie or TV show without ever building a physical model of a space ship.
But I would think some models from earlier shows and movies would be desirable, to some, to have on display (or even in a private collection).
What happened to the models from the original Star Trek? I don't mean every single model, but do we know what happened to the Enterprise? How about the original Klingon or Romulan ships? And, as for the shuttlecraft, is there any information on what happened with the model or the mock-up exterior?