The Collaborative International Dictionary of English v.0.48:

Outgrow \Out*grow"\, v. t. [imp. Outgrew; p. p. Outgrown; p.
   pr. & vb. n. Outgrowing.]
   [1913 Webster]
   1. To surpass in growing; to grow more than. --Shak.
      [1913 Webster]

   2. To grow out of or away from; to grow too large, or too
      aged, for; as, to outgrow clothing; to outgrow usefulness;
      to outgrow an infirmity.
      [1913 Webster]

WordNet (r) 3.0 (2006):

outgrow
    v 1: grow too large or too mature for; "I have outgrown these
         clothes"; "She outgrew her childish habits"
    2: grow faster than

Moby Thesaurus II by Grady Ward, 1.0:

31 Moby Thesaurus words for "outgrow":
   blossom, brew, burgeon, develop, flourish, gather, germinate, grow,
   grow up, hypertrophy, increase, mature, mushroom, overdevelop,
   overgrow, overtop, procreate, pullulate, reproduce, shoot up,
   spring up, sprout, sprout up, thrive, tower, upshoot, upspear,
   upspring, upsprout, vegetate, wax