  The projectivised nilpotent orbit closure P(\bar{O}) carries a natural
contact structure on its smooth part. A resolution X \to P(\bar{O}) is called
contact if the contact structure on P(O) extends to a contact structure on X.
It turns out that contact resolutions, crepant resolutions and minimal models
of P(\bar{O}) are all the same. In this note, we determine when the
projectivised nilpotent orbit closure admits a contact resolution, and in the
case of existence, we study the birational geometry among different contact
resolutions.
