Originally Posted by
Q Shoe Guy
JR East(JR東日本） runs all Shinkansen NORTH of Tokyo.
JR Central (JR Tokai) runs all Shinkansen between Tokyo and Shin-Osaka.
JR West runs all Shinkansen from Shin Osaka to Hakata (this will change in March 2011, with the opening of the Kyushu Shinkansen).
Some of the 700 series train sets (all N700 series) have green cars (often 16 cars long). As others have pointed out you can use these trains when they run as Hikari with your green train pass.
Err... what I meant is the trains owned by, not run by. You are quite correct that the different JR companies swap train crews depending on the segment of the Shinkansen, although the train set may be owned by another JR company.