The Collaborative International Dictionary of English v.0.48:

Blastostyle \Blas"to*style\, n. [Gr. blasto`s sprout, bud + ? a
   pillar.] (Zool.)
   In certain hydroids, an imperfect zooid, whose special
   function is to produce medusoid buds. See Hydroidea, and
   Athecata.
   [1913 Webster]