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Board 1: North opens 1H on K10x AQ10xx xx A9x. East may pass or bid a weak 2S on A9876x xx Jxx xx; my standard for a weak jump overcall is essentially the same as a weak two opening and this does not qualify. It isn't that I don't think such a bid can gain; but I think it's more important to jump with, say, AQJxxx and a side King, and too wide a range can pose insoluble problems for partner. Opposite a passed hand, I'd be more inclined to jump.
South has a monster: Jx KJ9 AKQx KQJx. The only question is "which slam?" Although hearts should be fine as trumps, might a 4-4 minor fit provide an extra trick for a grand slam? Probably not in this case: you'd need partner to have three Aces and the Queen of hearts, which would produce 13 tricks at notrump. If you had a side suit like Axx or AKxx, it might be useful to make another suit trumps and pitch losers on the hearts.
A straight jump to 4NT is a fairly practical bid here. There's a slight chance of two quick spade losers, but there's also the chance they fail to lead spades. 6NT, however, may play better from partner's side if he holds Kx(x) of spades, so a temporizing bid of 2D has some merit. All in all, though, I think 4NT directly over 1H is the simplest approach, aiming for 6H. Partner's reply shows 2 Aces or 2 key card + the Queen, and 6H makes easily.
Over a 2S jump, South cannot ignore the sapde problem; best is a 3S support-showing cue-bid. North bids 4H and South continues with 5D, a control cue-bid. North has control of both clubs and spades and has no trouble bidding 6H. When partner goes beyond game to make a slam try, don't worrry about overall strength, the only issue is controls.
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