Power Grid: Auction in following rounds
In all of your cases A chooses the next power plant. The rules are quite clear: 


  When a player other than the player who started
   the auction wins the auction, the auctioning player may choose a new plant to auction from the actual market or pass


A will keep putting power plants up for bid until either


A wins a power plant auction
A passes (and is out for the entire phase, they will not get a power plant this turn)


Remember, that when choosing a power plant A must make the first bid for at least the minimum printed on the power plant card.