Your partner opens 1NT, and you transfer to hearts. You now bid 3NT, and partner bids 4C, obviously a cue with extras and heart support. (This was an auction from a BBF discussion.) What should 4D mean by you?
This is sort of a strange auction. Ideally, if Responder held three spades, with slam interest, he might have considered a manufactured 3C call rather than 3NT, which has a lot going for it. You might find the heart fit early, and you might find a 3-5 spade fit if partner rebids 3S. That is usually my call.
So, if Responder is interested here, he almost assuredly does not have 5H/3S, in my opinion, as 3NT just seems wrong with that. Also, with slam interest and a 4-card major, why not mention that? So, if Responder has any interest, he has precisely 2-5-3-3 shape, it would seem.
Now, obviously this is not universal, as many would not bid a faker 3C with 5332, wherever the doubleton might be. I think that is a mistake, but whatever. One thing is for sure, though -- Responder just cannot logically have a stiff anywhere. That would be too weird, to bid 3NT with some 5431 and slam interest.
4D is often treated as Last Train, which makes some sense. But, Last Train might be somewhat subject to interpretation in this sequence.
This auction is rather pinched. Opener only had two possible cues -- 4C and 4D. Looking at a club control, he obviously had to bid 4C. But, there is no space available to cue both diamonds and spades without bypassing 4H. Plus, the specific situation is one where the only true cue available did not deny anything, meaning that two suits could not be shown control-wise.
In this situation, it makes some sense to think of 4D as not just "Last Train" but rather as "Cue-Enabling Last Train." In other words, 4D shows sufficient values that if Opener is still interest he might continue cuebidding into the five-level safely, whether cue of 4S or of 5D.
This nuance might come up ion other sequences, as well. I mean, technically one might look at a forcing pass of 4S by the opponents, after agreeing hearts, might be a "Cue-Enabling Forcing Pass."
Responder has an unlimited hand at this point. But, a fit is agree, and only one call is available below 4H to seek slam -- 4D. That call might be construed as Last Train, but also as Cue-Enabling Last Train, to encourage entering the five-level to make cuebids.
The nuance to this is that this QE-LTTC call is one that invites slam where control cannot be established yet. As such, it strongly suggests considering cues at the five-level rather than simple RKCB, and it likely also erases any default agreements suggesting Exclusion RKCB or other asking bids.
In some situations, this QE-LTTC might not actually say, "Do you have extras?" Rather, consider the original auction that started this discussion. Opener showed extras already. So, the QE-LTTC call could also be one of captaincy. "Huh?" Yep. Responder might want to control the auction and might therefore bid a QE-LTTC to induce partner to continue describing his hand rather than describing the other way. In other words, whereas Responder might cue 4S to ask for a diamond control, or 4D and then keep bidding to infer the need for a spade control, a QE-LTTC approach has 4D induce Opener to keep describing, maybe because Responder knows more already or something like that, especially if this occurs in a different auction. In some situations, this might even be construed as a "Cue-DEMANDING Last Train," or QD-LTTC.
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