An empathetic splinter is typically a bid of a worthless fragment to show great values everywhere else and worthiness of slam IF partner has a stiff in THIS suit.
An "auto splinter" is a splinter made in "support" of your own suit, such as a jump to 4♦ after transferring to hearts.
What about an "Auto Empathetic Splinter?" A bid of a worthless fragment, expressing the need for a specific stiff if partner can support your own suit? Yep, the beast exists.
The idea arose from a problem at BBF ("matmat" proposed the problem). You have ♠Kx ♥Jxx ♦Ax ♣AKxxxx and open 1NT. Partner bids 2♣ Stayman, and you obviously respond 2♦. Partner bids 2NT, invitational. What now?
The vast majority responded with something like "3NT. What's the problem?"
But, give partner decent club support, a stiff heart, the spade Ace, and maybe the diamond King. It is easy to construct hands for partner where 6♣ is a very strong bet.
So, why not bid 3♣? The concern is that zooming to 3NT avoids helping the defense make a lead. Fair point, but I doubt that a club lead was coming, anyway. The 3♣ bid, therefore, probably does not help much. Responder bidding stoppers might, though. So, perhaps 3♣ should simply be a natural call expressing uncertainty, suggesting a hole, and asking a conditional question:
"If you have an unbalanced hand and support for my clubs, bid your shortness."
The parallel is a 3♦ call from Opener, instead of 3♣. As only 3♥ and 3♠ are available for Responder, however, a 3♦ call would suggest long diamonds and a worthless holding (for notrump) in one of the majors -- an either-or empathetic splinter if you will. A 3♦ call, then, announces a different question:
"If you have support for my diamonds and shortness in one of the majors, indicate your short major."
If Opener has diamonds and interest in short clubs from Responder, he can bid the cheapest unbid major. Thus, for instance, after the example auction of 1NT-2♣-2♦-2NT, Opener could bid 3♥ as an "Auto Empathetic Splinter," showing long diamonds and a worthless club fragment.
I say "the cheapest unbid major" to cover 1NT-2♣-2M-2NT sequences. Opener could rebid his own major because he has five of them. If Opener bid 2♠, then 3♠ is natural (five-card suit) but 3♥ could be the Auto Empathetic Splinter, with diamonds and a stopper hole in clubs. If Opener bid 2♥, and if 3♠ is not needed to handle 4-4 majors, then 3♠ would serve that function. Obviously, in this latter situation the diamond suit will be shorter because of the obvious length in the bid major.