Oh, good questions, though this might wind up a long answer to a short question.
In most circumstances, the hawk doesn’t carry the prey, for a couple different reasons. First of all, we train them to “go to ground” with quarry, which basically means that when she nails something, she pins it down to the ground, hangs on for dear life if it’s not already dead, and waits for backup to arrive. This is in direct opposition to what they’d normally do, which is to target the easiest prey and get up off the ground as quickly possible. Sitting on a jackpot prey item (particularly a partly-incapacitated, bleeding and flailing one) is like a neon sign to other predators that lunch is on. However, if she were to pick up and carry her catch, there’d be no way I could be on the spot to assist in the dispatch if she needed help, and frequently she does.
Secondly, the primary goal in all of this is to be catching larger, better-quality game than the hawk is capable of catching and killing on her own. That’s part of the benefit of sticking with me–in the wild most of her meals would be mice, voles, little stuff. She eats a whole lot better with my help, which is why she makes the choice to hunt in a cooperative partnership. An adult rabbit or hare is much too big for her to pick up and carry away, and much of the time too big for her to kill on her own. What they do catch they don’t usually eat much of right then and there; once they’ve eaten, they’re done hunting for the day. Also, we discourage them from hunting snack-sized critters because what happens in that case is that the hawk goes up to the top of a greeeeat big tall tree, packs her crop full, tucks one foot up snugly in her breast feathers and stays put for the next two days (curses), and also packrats just don’t make good eatin’, relatively speaking ;).
The problems around catching carrying-sized prey is also why fishers like sea eagles (balds) and osprey don’t make good falconry partners. They yoink their prey right out of the water and up into the nearest tree–my services would be of no benefit to them.
“Carrying” is mostly considered a vice for the reasons mentioned, though folks practicing sparrowhawking or chasing similar quarry will frequently train the pocket-sized longwings to carry to glove with their catch. Spotting a teentsy little falcon on the ground can be difficult in any kind of cover.
The answer to the question about what they can be trained to catch depends on the species, the falconer, and the individual bird. In the US we are fortunate to have an abundant, hardy, extremely versatile game hawk in the red-tailed hawk. A good red-tail is just about as good as it gets in terms of a hunting partner. They are brave, strong, sizable enough to take on most quarry, and game enough to chase down just about anything they think they can kill (and a few things they certainly can’t, but will sure take a stab at). As Xema said in the other thread, they are somewhat lacking in “exotic” sex-appeal which matters to some people, but for a hunting partner there’s just about no better hawk anywhere in the world.
US falconers fly RTHs over everything from rats and rabbits to squirrels, game birds, waterfowl, even foxes. Each type of quarry demands a totally different set of hunting skills and talents. The reason it is so notable for a RTH to be versatile in that way, is that mostly raptors are very specialized birds–like little, feathered hunting machines finely honed to a very specific task. Most species will target either fur or feathers but not both, and within those groups most species will target whatever quarry they’ve evolved to chase. Entering a bird to “nontraditional” quarry (training it to catch things it wouldn’t likely chase in the wild) is sometimes a hallmark of serious success.
On the topic of yorkies, well, that’s a tricky one. I wouldn’t expect, say, a gyrfalcon tuned in to waterfowl to show the slightest interest in a little, scurrying brown dog. If I saw one running around while in the company of a goshawk or RTH I’d be hanging on tight to the jesses for the reasons mentioned above, though the likelihood of encountering a small pet dog on a hunt is not high. We try to curb the tendency to chase non-game (or more properly non-quarry) species by keeping a tight hold on them any time we’re around anything we don’t want them to chase, and rewarding them for chasing the things we do.
