In a recent entry my preliminary conclusion was that 10.fxe3 Nxe3 11.Qb3 Nxg2+ 12.Kd1 doesn't look like a clean winning line. Consequently it seems sensible to examine White's alternative king move, 12.Kf2. Even if alternatives have been tested, I will assume that 12...Bh3 (Dia) is the critical test. Black develops another minor piece while protecting his advanced knight.
13.d4
This looks natural.
a) White should avoid 13.Rg1? Bc5+.
b) Unsurprisingly 13.Bf1 also fails: 13...Bc5+ 14.Kg3 Qd7 15.Qc4 Nd4 16.Nxd4 Qg4+ 17.Kf2 (Gross-Grehl, corr 1991) 17...Qf5+! 18.Kg1 Re8 and Black is winning.
c) 13.Bc4 Qe7 (13...Bc5+ 14.Kg3 Qd7 15.Bxf7+ Kh8 16.Qc4 Rf8–+ Alvarez-Roldan, corr 1998) 14.Bxf7+ Kh8 15.Bd5? Bc5+ 16.Kg3 Qd6+ 17.Kxh3 Nf4+ also wins for Black Nebe-Vorlop, corr 1988.
d) 13.Kg3 looks suspect and 13...Qd7!? probably is sufficient:
d1) 14.Ng5 Bd6+ 15.Kf2 Qf5+ 16.Nf3 (or 16.Bf3 Bc5+ 17.Ke2 Qxg5) 16...Bc5+ 17.Kf1 Nf4+ 18.Ke1 Re8 and Black wins.
d2) 14.Ne5 Bd6 15.d4 Nxe5 16.dxe5 Be7 17.e6 Bxe6 18.Qd3? Bd5 was winning for Black in Seifert-Nebe, corr 1991.
d3) 14.Qc4 b5 15.Qxb5 Bd6+ 16.Kf2 Rb8 17.Rc1 Rxb5 18.Bxb5 Qf5 –+ Gross-Grehl, corr 1992.
d4) 14.Ng1 Bd6+ 15.Kf2 Bc5+ 16.Kg3 Bxg1 17.Rxg1 Qd6+ 18.Kxh3 Nf4+ 19.Kg4 Nxe2
e) 13.Rd1 Qe7 14.Ba3 (14.Ng1? Bc5+ 15.d4 Nxd4 16.Rxd4 Qh4+ 0–1 Zschalich-Leisebein, corr 1987) 14...Re8 (14...Nd4!? 15.Qd3 Bxa3 16.Nxa3 Nxe2 17.Qxe2 Qxa3 with advantage to Black could be an improvement) 15.Bf1 g5 16.Bxb4 Nxb4 17.Na3 g4 18.Re1 Nxe1 19.Rxe1 Qc5+ 20.d4 Rxe1 21.Bxh3 Re2+ 22.Kxe2 gxf3+ 23.Qxf3 and White was slightly better in Zschalich-Preussner, corr 1997.
This is the critical moment. White is relatively free to improve his position but nothing looks particularly convincing.
14.Ne5
a) After 14.Bc4? Na5 15.Bxf7+ Kh8 Black was winning in Gedigk-Grehl, corr 1990.
b) 14.Nbd2 is strongly met by 14...Bxd2 15.Nxd2 Nxd4 16.Qxh3 Qxe2+ 17.Kg3 f5 18.Rhf1 (18.Qxg2 f4+ 0–1 Ritter-Reyes, corr 1996) 18...f4+ 0–1 Oakes-De Smet, corr 1992.
c) 14.Na3?! Re8 15.Ne5? Nxe5 16.Qxh3 Nf4 was winning for Black in Perrson-Grehl, corr 1989.
d) 14.Rg1!? deserves a look.
e) 14.a3 should be taken seriously as it has been tested by one of the real experts: 14...Re8 15.Bc4 Na5 16.Qxb4 (16.Bxf7+ Kh8 17.Qd5 Qe2+ 18.Kg3 Ne3 –+) 16...Qe3+ 17.Kg3 Qf4+ 18.Kf2 Qe3+ 19.Kg3 h5 –+ Trokenheim-Ronneland, Sweden 1994.
14...Nxd414...Nf4!? may be an improvement. 15.Qxf7+ Qxf7 16.Nxf7 Nxe2 17.Nh6+ gxh6 18.Kxe2 Re8+ is clearly better for Black.
15.Qxf7+ Qxf7+ 16.Nxf7 Nxe2 17.Ng5 Bc5+ 18.Kxe2 Nf4+ (Dia)
Black still has only got three pawns for his rook but White's king is exposed and his rooks are exposed in their corners.
19.Kd1?!
Giving back the exchange with 19.Kf3 Bg2+ 20.Kxf4 Bxh1 looks fairly balanced but Black may have less losing chances.
19...Rd8+ 20.Kc2?
This seem to lose. 20.Nd2 doesn't look safe at all and I suspect a good PC programme would find something for Black if given some time and gentle guidance (but 20...Bg4+ 21.Kc2 Bf5+ 22.Nge4 Be3 23.Rhd1 Rxd2+ 24.Rxd2 Bxe4+ 25.Kd1 Nd3 26.Bc3 b5 is only a little better for Black).
20...Bf5+ 21.Kb3 h6 0–1 Zschalich-Poetzsch, corr 1987 (22.Nf3 Rd3+ –+)
Conclusion:
Based on available games and some quick checks by Fritz and Rybka, 12.Kf2 looks even less convincing than 12.Kd1. It probably will pay for both sides to examine alternatives to 11.Qb3 - that is 11.Qc1 and 11.Qa4.