Singleton Aces

At least 3 times last night I held a singleton A in a suit partner held a lot of cards with the KQ and very few if any entries. This one deal I still don’t know how to bid.

♠ x ♥ T9xxx ♦ xx ♣ KQJ9x

♠ AKQJT ♥ A8x ♦ KQ9x ♣ A

What contract would you want to be in? 4H, 3NT, 4S, 5C, 6C? Is the north hand good enough for a positive 3C after south opens 2C? After the auction starts 2C-2D (art gf); 2S, should north rebid 3C or 3H? It’s an awkward deal. Emory rebid 3H and I was perhaps a bit over-aggressive and bid 4NT, which brings up another question. Playing kickback, should 4NT be natural quantitative or key card? Could 4S reasonably be natural? South had so many other ways to show 1-suiters with spades that 4S should probably be key card and 4NT quant.

♠ Qxx ♥ AT98x ♦ xx ♣ Axx

♠ AKT98 ♥ KQ ♦ AKQxx ♣ J

This one I knew how to bid. We got to the grand in spades but what’s the percentage play to make on a spade lead with a 4-1 split (RHO has Jxxx)? So many options: ruff a diamond in dummy, draw trumps and play for HJ to drop, falling back on 3-3 diamonds if needed, unblock KQ, cross to dummy to ruff a heart and establish a long heart to discard the last diamond potential loser. All lines were winners on this layout. Someone want to workout the exact percentages for me, just for fun?