The Collaborative International Dictionary of English v.0.48:

Predominant \Pre*dom"i*nant\, a. [Cf. F. pr['e]dominant. See
   Predominante.]
   Having the ascendency over others; superior in strength,
   influence, or authority; prevailing; as, a predominant color;
   predominant excellence.
   [1913 Webster]

         Those help . . . were predominant in the king's mind.
                                                  --Bacon.
   [1913 Webster]

         Foul subordination is predominant.       --Shak.
   [1913 Webster]

   Syn: Prevalent; superior; prevailing; ascendant; ruling;
        reigning; controlling; overruling.
        [1913 Webster]

WordNet (r) 3.0 (2006):

predominant
    adj 1: most frequent or common; "prevailing winds" [syn:
           prevailing, prevalent, predominant, dominant,
           rife]
    2: having superior power and influence; "the predominant mood
       among policy-makers is optimism" [syn: overriding,
       paramount, predominant, predominate, preponderant,
       preponderating]

Moby Thesaurus II by Grady Ward, 1.0:

93 Moby Thesaurus words for "predominant":
   all-absorbing, arch, ascendant, at the head, average, banner,
   besetting, boss, capital, cardinal, central, champion, chief,
   commanding, common, controlling, crowning, current, dominant,
   epidemic, first, focal, foremost, general, governing, great, head,
   headmost, hegemonic, hegemonistic, highest, important,
   in ascendancy, in charge, in chief, in the ascendant, influential,
   leading, magisterial, main, major, master, normal, number one,
   on the throne, ordinary, outstanding, overbearing, overriding,
   overruling, pandemic, paramount, popular, predominate,
   predominating, preeminent, premier, prepollent, preponderant,
   preponderate, prepotent, prevailing, prevalent, primal, primary,
   prime, principal, rampant, ranking, regnant, regulating,
   regulative, regulatory, reigning, rife, routine, ruling, running,
   sovereign, standard, star, stellar, stereotyped, supereminent,
   superior, supreme, swaying, telling, topflight, topmost,
   transcendant, uppermost, usual