Here being a piece up I would have tried 19 Qd4+ followed by Bd3. Then I would have continued with the standard pawn storm on the kingside. Even if Black pried open the a file, White's king simply escapes via d2 and forces more rook exchanges. There really isn't anything Black can do. Whereas in the game, white ended up with lots of pressure on White's king.

id=dmaestro makes a lot of sense, but his is just one plan among many White could adopt here. I rather like the prophylaxis behind White's move, which reduces Black's counterattacking chances on the Q-side practically to nil. I'm inclined to think it was the follow-up gave Black more play than he really deserved. All the same, Black's next is in keeping with his planned counterattack.

White need not have been so defensively minded after 19...a4: 20.Qd4+ Kg8 21.Qd5, with huge pressure on Black's game. Against 20...f6 21.Qd5 is still good. *** After the moves played: 19...a4 20.Kb1?! axb3, I prefer 21.Bxb3, defending the sensitive spots at a2 and c2 comfortably enough, and eyeing f7 as well. Black's possession of the open files looks imposing but the isn't much he can do to improve his position. Once her K is secure, White has plenty of room to build an irresistable attack.*** Having said all that, White still has all the advantage in the diagrammed position. Black's Q-side pressure isn't discommoding White very much ... yet! 23.Rd5, with a view to doubling rooks on the d-file looks strong.

White had a number of good options, but should have been more active.

Black has been given some leeway and hence some hope. Probably better for White would have been to double rooks on the d-file at move 26 (26.Rcd2) with pressure on the d6-pawn. It can't advance (26.Rcd2 d5? 27.exd5 exd5 28.Rxd5 Rxd5 29.Rxd5 with a strong attack [the BQ has to defend d8, so 29...Qb6 30.Qd4 just about forces the Qs off, leaving Black without a prayer]). But if Black defends it with R or Q, his attack down the a-file dies away.

A different approach was 28...d4, which cuts off the long diagonal, and threatens further advance. But Black certainly had to give his K some air, owing to White's ownership of the long diagonal, and the threat of Rc8 at some point. Black is in fact running out of play. White's huddle of major pieces on the Q-side conceals quite a bit of "aggro"!

You made an appropriate move. By no means would I expect an opponent to ever offer draw in a position like this. You're up a minor piece and a pawn, so this is textbook stuff. I'm commenting on this as close to "real time" as I can, looking through this game. But that black b pawn should be an instant focus of your attention, with its fall meaning the ultimate push of your two past kingside pawns.

A draw offer by White is out of the question: White is winning, pure and simple. To be sure, an extra piece and pawn is no sure guarantee of victory, even so late in the game, but Black really has no play, not least because White is admirably centralised to cover all possible entry points there and on the flanks. OK: how to translate this into victory? For a start, White can take her time: no need to rush. However, her last move, quiet and patient as it is, carries a nasty threat. Black's offer to exchange rooks isn't so surprising.

Lucky you! Black has presented you with gifts the whole way through. No big deal that the queen was defensive in the midgame (which is actually rather appropriate, since attacking on the frontlines is work better delegated to the minions), since you were basically able to sit back and reap the rewards of these kinds of errors.