I have posted my thoughts and research here as well http://alaunts.wordpress.com/2014/05/10/alaunt/ and I guess the next Alaunt type I will post about is the "Alaunt Gentil". In shape I consider the game bred apbt to be the closest canine to the Alaunt Gentil of the middle ages.

"And the good alauntes be those which men call alauntes gentle. Others there be that men call alauntes veutreres, others be alauntes of the butcheries. They that be gentle should be made and shaped as a greyhound, even of all things save of the head, the which should be great and short.
For the good alaunte should run as fast as a greyhound, and any beast that he can catch he should hold with his seizers and not leave it. For an alaunte of his nature holds faster of his biting than can three greyhounds the best any man can find. And therefore it is the best hound to hold and to nyme (seize) all manner of beasts and hold them fast. And when he is well conditioned and perfect, men hold that he is good among all other hounds. But men find few that be perfect. A good alaunte should love his master and follow him, and help him in all cases, and do what his master commands him. A good alaunte should go fast and be hardy to take all kinds of beasts without turning, and hold fast and not leave it, and be well conditioned, and well at his master's command, and when he is such, men hold, as I have said, that he is the best hound that can be to take all manner of beasts." Gaston Phoebus