With all the heavy pieces on the g-file, intuition tells us Black will break through there somehow, and then deliver the coup de grâce by means of a threat incorporating mate on it and the h-file. It's just a matter of how to begin.

<<•> 32. ...Bxh3! >

White must either recapture or take the rook on g3; anything else merely allows Black to take a critical defensive pawn for nothing.

< (1) 33. Bxh3, Ng4†

34. Bxg4 ... >

Not to be countenanced is (a) 34. Kh1?, Rxh3† 35. Kg1/g2, Nf2†! 36. Kxf2, Qg2#.

< 34. ...Qxg4 >

Black threatens 35. ...Qh3#, forcing White's next.

<35. Bxg3, Qxg3†
36. Kh1, Qh3†
37. Qh2, Qxf1†
38. Qg1, Qxg1# >

So much for taking the bishop. How about the rook?

<<•> (2) 33. Bxg3, Qxg3† >

White has two retreat squares.

<<•> (2.1) 34. Kg1, Ng4 >

Black threatens mate with 34. ...Qh2. Some rook move is necessary to give the king room to run.

< (2.1.1) 35. Rf2, Qh2†
36. Kf1, Qh1†
37. Ke2, Bxg2 >

Black already has two pieces and an advanced passed pawn for a rook, and will soon win the exchange, leaving him over a piece to the good.

< (2.1.2) 35. Rf3, Qh2†
36. Kf1, Qh1†
37. Ke2, Qxg2†
38. Kd1/d3, Qxf3 >

Black is two pieces ahead.

<<•> (2.1.3) 35. Rfb1, Qh2†

36. Kf1, Qh1†

37. Ke2, Qxg2† >

This may be relatively best for White, but Black again has two pieces and an advanced passed pawn for a rook, and White's king is not yet safe.

If not one retreat, what of the other?

< (2.2) 34. Kh1, Ng4 >

To avoid mate on h2, White must move the bishop.

< (2.2.1) 35. Bxh3?, Qxh3†
36. Kg1 ... >

No better is (a) 36. Qh2, Nxf2 37. Rxf2 (else the knight discovers mate), Qxf1#.

< 36. ...Nxe3†
37. Kf2, Qxf1†
38. Kxe3, Rg3†
39. Kd4, Qc4# >

Perhaps another bishop move?

< (2.2.2) 35. Bf3, Bxf1 >

My second line was: <32...Bf3> 33.Rxf3 Rxf3 34.Bxh4 Rxh3+ 35.Kxh3 Qg4+ 36.Kh2 Qxh4+ 37.Kg1 Ng4 when I found the moves again aren't forced, but this seems stronger than line #1

My third line was: <32...Bf3> 33.Bxg3 Qxg3+ 34.Kh1 Qxh3+ 35.Kg1 Bxg2 36.Qxg2 Qxe3+

click for larger view

I thought this looked pretty good

White threatens hxg5 and Bxg3.

The bishop blocks the action of the other pieces. This invites to play 32... Bxh3:

A) 33.Bxh3 Ng4+

A.1) 34.Bxg4 Qxg4 (threatens Q(R)h3#) 35.Bxg3 (35.Kh1 Qh3+ 36.Qh2 Qxf1+ 37.Qg1 Qxg1#) 35... Qxg3+ 36.Kh1 Qh3+ 37.Qh2 Qxf1+ 38.Qg1 Qxg1#.

A.2) 34.Kh1 Rxh3+ 35.Kg2 (35.Kg1 Nf2+ 36.Kxf2 Qg2#) 35... Nf2+ 36.Kf3 Qg4+ 37.Kxf2 Qg2# (or 37... Rh2#).

B) 33.Bxg3 Qxg3+

B.1) 34.Kh1 Ng4 35.Bxh3 (35.Bf3 Bxf1 - +) 35... Qxh3+ 36.Kg1 Nh2+ 37.Qg2 (37.Kh1 Nxf1+ 38.Kg1 Nxd2 - +; 37.Kf2 Qxf1#) 37... Rxg2+ 38.Rxg2 Nxf1 - + [Q+P vs R].

B.2) 34.Kg1 Ng4 (threatens 35... Qh2#)

B.2.a) 35.Rf3 Qh2+ 36.Kf1 Qh1+ 37.Ke2 Qxg2+ 38.Kd1 Qxf3 - + [B+N+P].

As an aside, you may remember this thread regarding Storrs from a while back:

32. ... Bxh3
33. Bxg3 Qxg3+
34. Kh1 Ng4
35. Bf3

Best from here, as far as I can tell, is:

to xray through in bishop hatcher gg on to 32.Bxh3,

shine out for me as the forge it candidate aimed duty anchor dead if I culture in shag pile down ingfile as it were in west side storey in light b-,