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Here is a game between a couple of the top-ranked players. White resigns rather than playing gxh3. My guess is that 31. gxh3 would be met with Qg3. Almost regardless of white's next move, black could play 32. ... Qxh3+. After that I'm not so sure - maybe start advancing the h pawn?
http://queenalice.com/game.php?id=965108
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Maybe Nh5 with threats that will let the passed pawn run.
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31.gxh3 Qh4 and white have no satisfactory defense.
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>31.gxh3 Qh4 and white have no satisfactory defense.
Against what? Black doesn't have a concrete threat, just a weak White K. I guess I must be missing something. How does Black proceed after the obvious 32 RxN ? Black does seem to have a strong position yes its not won yet. I would have thought worth fighting on at least to see how the position evolves over the next few moves?
Is it already lost?
Steve
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I imagine that after the h-pawn is captured with check there is a rook lift to e5 but I haven't calculated detailed variations. 
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31.gxh3 Qh4 32.Rxf6 (gxf6 33.Rg1+ and 34.Kh2),Qxh3+ 33.Kg1 gxf6 34.Qxf6 Re6 36.Qd8+ (...Kg7 37.Qd4+ {...Kg8 or f8,h8 seems a drawn}...Kg6 38.Bd3+ Kh6 39.Qxf4 too seems a drawn game)so... 33...gxf6? ...Its better 33... Te5! threatening Mate 34.Qa5 Rxa5 35.bxa5 gxf6 36.a6 Be8 37.a7 Bc6 38.Rd1 Qg3+ 39.Kh1 Qf2 40.Rd8+ Kg7 41.a8=Q Bxa8 42.Rxa8 Qxe2 and the black pawn advanced deciding the game. 0-1 
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