[mikl_plkcc]

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Now I need to show game-force support in ♠, but lacking agreement after unusual 2NT I didn't know what to do so I passed, and waited for the opponent to act.

So what does 3♣ or 3♦ normally mean here?

After passing, the auction now went:

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Does this sequence show exactly 3 ♥? Is it possible for the responder to have 2 only?

Now there was obvious slam interest. My main concern was if I would lose 2 ♦ tricks. Therefore I started cuebidding.

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What's the correct bid here? The only unknown now is the ♥A and ♦K.

[DavidKok]

A relatively common treatment is "Unusual over unusual" - where you could bid 3♣ to show a strong hand with hearts, 3♦ to show a strong hand with spades, 3♥ to show a weaker (merely competitive) hand with hearts and 3♠ ditto for spades.

I would, without agreements indicating otherwise, interpret jumps over their 2NT as splinters agreeing spades, so 4♣ would be a nice bid.

4♥ should show at least 3 hearts, otherwise partner could double instead.

As for the last bid, I'd try 6♣, showing a void and asking for extras. 5♦ would not promise the ace for me, so you may well be off one quick trick.

[AL78]

A simple way of dealing with the unusual NT in this sort of auction is as follows:

1♥ - (P) - 1♠ - (2NT)
?

3♣: Mod/Strong opening hand with hearts.
3♦: Mod/Strong opening hand with spade support.
3♥: Weak opening hand with long hearts.
3♠: Weak opening hand with spade support.
X: Penalty interest in at least one of the minors.
Pass: Weak opening hand without spade support or long hearts.

In the sequence you give where partner jumps to 4♥, it sounds like partner has a decent hand with three hearts and four or five spades, in which case you have a massive double fit. In that case, I would have expected much more of a barrage from the opponents as after the 2NT bid, East will immediately know they have a massive double minor fit.

Once partner cues a diamond control (presumably a first round control), I'd probably just bid 6♥. Ideally I would have liked to show a good hand with spade support earlier, then there probably exists some two suited key card Blackwood convention that can be wheeled out, or bid 5NT pick a slam.

[LBengtsson]

it is 6502 with good ♠ support. just bid 4♣ splinter. 65 hands are very distributional strong. in support of ♠ this hand is 18/19+ count. tell partner the good news by a splinter

[nige1]

mikl_plkcc 'Now I need to show game-force support in ♠, but lacking agreement after unusual 2NT I didn't know what to do so I passed, and waited for the opponent to act. So what does 3♣ or 3♦ normally mean here?'
+++++++++++++++++++
I rank:
1. 4♣ = SPL agreeing ♠.
2. 3♦ = CUE agreeing ♠.
3. 5♠ = NAT suggesting 2 ♦ losers.

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mikl_plkcc ' After passing, the auction now went: What's the correct bid here? The only unknown now is the ♥A and ♦K.
++++++++++++++++++++

IMO passing 2N was brave East might take a view and pass
Now, I rank:
1. 7♠ = Punt but 5♦ is likely to show 1st round control.
2. 6♠ = Safer.

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[mikl_plkcc]

nige1, on 2021-October-01, 16:10, said:

mikl_plkcc 'Now I need to show game-force support in ♠, but lacking agreement after unusual 2NT I didn't know what to do so I passed, and waited for the opponent to act. So what does 3♣ or 3♦ normally mean here?'
+++++++++++++++++++
I rank:
1. 4♣ = SPL agreeing ♠.
2. 3♦ = CUE agreeing ♠.
3. 5♠ = NAT suggesting 2 ♦ losers.

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mikl_plkcc ' After passing, the auction now went: What's the correct bid here? The only unknown now is the ♥A and ♦K.
++++++++++++++++++++

IMO passing 2N was brave East might take a view and pass
Now, I rank:
1. 7♠ = Punt but 5♦ is likely to show 1st round control.
2. 6♠ = Safer.

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5♦ guarantees 1st round control in our agreement (we bid 1st before 2nd) - is 7♠ good?

[Lovera]

I would be of the opinion that the opponents are short in the major suits. As developed, N's bid would appear to be of the type 2/1 with the fifth Spades at the K in a balanced hand. The lack of 2NT Jacoby suggests that there are no conditions and, therefore, N may have the third Hearts to the Ace. The two hands would therefore combine very well, thus having the suit of Hearts to discard any possible losers.