I think the north hand has a very tough call at round 2. There are arguments, of varying degrees of soundness, for:
2
♣: obviously best if one plays a version of Gazilli or Cole, but some would advocate it even without these agreements: one of the commentators on vugraph said that Kokish would surely bid 2
♣. It is not quite as silly as it may sound, because of the inadequacy of the alternatives
3
♣: probably the consensus expert choice: this hand is a minimum, perhaps even a sub-minimum for a game force when the hearts are suspect, we don't have real clubs, and we have a stiff in partner's suit. Adam noted that some players (me amongst them) use 3
♣ as artificial... after opening 1
♥, the jumpshift shows either very good hearts or real clubs... the problem is that this hand isn't really either
2N: this distorts the major suit length, but is otherwise right on values... however, the distortion is probably unacceptable to most players.
3
♥: this gets the heart suit into context and doesn't distort the shape, but could be bid with a full King less, so is a major strength distortion
Assuming no agreement that 2
♣ is forcing, I'd rank the calls as 3
♣ 100, 2N 80, 2
♣ 60 and 3
♥30.
As for what responder is to bid: 3
♦ over 3
♣ seems normal, even if it is probably futile... it's main benefit is to allow opener to suggest the denomination... and that will NOT include diamonds, since 3
♦ would not, to most experts, promise a suit... it is a stall. Opener might, for example, be 3=5=1=4 or 3=6=1=3 etc and now we get to spades.
As for the 3
♥ rebid by opener.. I'd prefer 3N with that hand.
Having seen the 3
♥ rebid, I'd think that 3
♠ would be the more popular choice compared to 4
♥ (with 3N a distant 3rd choice), but I don't think that 4
♥ is horrible.
As for the poster who claimed that they'd respond 2
♦ and then, over 3
♥, rebid 3
♠ and find their way to 6
♦...... if intended as a joke, well done.. if intended seriously... well, your methods are certainly a long, long way from mainstream
'one of the great markers of the advance of human kindness is the howls you will hear from the Men of God' Johann Hari
3h-4h-ap