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The 'woody rook' has 5 linearly contiguous squares, counting itself when guarded by the king. I was looking at the pattern of the move: not just linear extension in 1 direction, but in 'both' directions, forward and back, or left and right. The king/guard projects a 3 square linear 'wall' around itself, and is thus invulnerable to a king. [The rook, or any rook analogue, interdicts the king over a range greater than the king can move around, but is still vulnerable to diagonal capture, so must be guarded by the king.] The BN and FAN do not have this property, even though either can mate a king in a corner without any other piece. [Possibly a severe head cold is affecting even my typing as well as higher-level functioning, but I was trying to say that my understanding of what has been discussed is that it requires a rooklike 'walling-off' feature of the piece to mate. It may not be sufficient, as a wazir has that feature, but right now, I'd have trouble mating a lone king with a king and queen, so I don't know whether K + W vs K is a win or draw - seems like it might be a draw, but I don't have the energy to find out...]