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how do you deal with those hannd types when opener responds 2♦ rather than 2♣ ?
You don't. Standard Bart only applies after 1
♠-1nt-2
♣. There is an article in Granovetter's
For Experts Only collection, that describes a possible artificial system after 2
♦ (along with a different version after 2
♣).
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If I agreed to play BART, does it mean that 5332 openers always rebid 2♣ even holding a doubleton ?
This is optional. If you do this, you will increase your chances to use the gadget, but you also increase chances of playing in some 2-3, 2-4 club fits, plus some 2-5 at 3
♣.
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And what should be opener's rebid holding 5 spades and 4/5 diamonds ? A natural 2D (which does not alow for accurate responder's description with BART) or an artificial 2C (to allow responder using BART) ?
You definitely want to bid 2
♦ with 4+ D. Bart already makes it hard to play in diamonds since responder can't show them at the 2 level. If opener can't show them either, you could be playing your 3-1 club fit instead of a 9 cd diamond fit :). You also make it harder for responder to raise clubs when appropriate.
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In both cases, a 2D rebid by opener would make it impossible for responder to differentiate his hand type, when holding a hearts-based hand.
Sure, but bidding 2
♣ always will almost certainly lose you too many minor partscore decisions to make up for the occasional gain in finding the 5-3 or 5-2 heart fits. If you are worrying about missing hearts, lower your requirements for 1
♠-2
♥ (i.e. don't play as GF), and/or let responder rebid 2
♥ on only 5 after 2
♦, let opener pull back to 2
♠ with stiff.