The Collaborative International Dictionary of English v.0.48:

coattails \coattails\ n. pl. [fig.]
   the influence of another person; the effect of association
   with another person; as, he was elected to office on the
   president's coattails.
   [PJC]

   on the coattails of
   (a) helped by association with another person. See
       coattails.
   (b) caused by, or immediately following (an event).
       [PJC]