When I was asked to explain RESTful service composition, and what I mean by staged computation and baton passing, I always need to find a concrete example instead of using abstract terms. Watching YouTube video across devices is a good case for this purpose.
A user can find a video on YouTube on her/his mobile device, and then continue play it on any other TV devices linked to YouTube. S/he can also stop/resume/skip on the mobile device or the current playing device. It is also easy to switch between linked active TV devices.
We can think the video play as a service composition. The goal of the composition is to play the video to the audience. The composition is composed of YouTube, the mobile device, and linked devices. The audience is the consumer of the composition.
Watching video across devices can be viewed as a RESTful service composition. The computation is the play of the video from user starting to watch one to stopping it. It can have several stages, each of which the video is played on one device.
When the video play is switched from one device to the other, the computational baton is passed. The next device continued the computation according to where the play should start from, and perhaps audience's other preferences. But the computation has to be adjusted according to the current device's resource, like screen size and bandwidth.
So is there a central conductor service? Maybe user's mobile device works like a conductor, but the playing of the video is in fact carried out by the linked devices and the mobile device itself. The linked device can also stop/resume/skip anytime.