The Collaborative International Dictionary of English v.0.48:

Profusely \Pro*fuse"ly\, adv.
   In a profuse manner.
   [1913 Webster]

WordNet (r) 3.0 (2006):

profusely
    adv 1: in an abundant manner; "they were abundantly supplied
           with food"; "he thanked her profusely" [syn:
           abundantly, copiously, profusely, extravagantly]

Moby Thesaurus II by Grady Ward, 1.0:

104 Moby Thesaurus words for "profusely":
   abundantly, acervatim, acutely, affluently, amazingly, amply,
   aplenty, astonishingly, awesomely, bigheartedly, bottomlessly,
   bounteously, bountifully, conspicuously, copiously, countlessly,
   diffusely, effusely, eminently, emphatically, exceptionally,
   exquisitely, extraordinarily, extravagantly, exuberantly, famously,
   freehandedly, freeheartedly, freely, fully, generously, glaringly,
   graciously, greatheartedly, handsomely, hospitably, immeasurably,
   impressively, in abundance, in crowds, in full measure,
   in good supply, in heaps, in plenty, in quantity, in throngs,
   incalculably, incredibly, inexhaustibly, infinitely, innumerably,
   intensely, largeheartedly, lavishly, liberally, magically,
   magnanimously, magnificently, markedly, marvelously, maximally,
   multitudinously, no end, nobly, notably, numerously, openhandedly,
   openheartedly, opulently, overflowingly, particularly, peculiarly,
   plenteously, plentifully, pointedly, preeminently, prodigally,
   prominently, pronouncedly, remarkably, richly, riotously, signally,
   singularly, splendidly, strikingly, superabundantly, superlatively,
   surpassingly, surprisingly, thickly, to the full, uncommonly,
   ungrudgingly, unselfishly, unsparingly, unstintingly, unusually,
   with both hands, with open hands, without stint, wonderfully,
   wondrous, worthily