The big heart condition in thoroughbreds is referred to as the "X-factor". From what I have read, stallions can only pass the big-heart gene to their daughters, but not their sons. But then the daughters can pass the gene to their sons, causing them to have big hearts.
So if Princequillo had a big heart, he no doubt got the gene from his dam, not his sire.
I guess the hot ticket is to mate big-heart stallions with daughters of other big-heart stallions, which should make it possible for the stallion's male offspring to have the big-heart condition from the mother's gene, and also improve the odds of the stallion's female offspring being homozygous for the big-heart gene. That (being homozygous) would improve the chances that the stallion's female offspring will have "big heart" sons when they are bred.
There's more to being a great thoroughbred than just the big-heart condition, like conformation, for example. But I can't imagine why a thoroughbred with the big-heart condition wouldn't be a better runner than he would have been without it.
