From my experience, they grab and do a short flight to a safe area to eat their prey. The hawks in my area have gone after rabbits, rattlers, cats, chickens, small dogs, you name it. It's quite the sight! Amazing birds!
I have a good friend that re-habs birds of prey. A hawk can not lift a 9 lb chicken. Hawks will kill and shred a chicken right there and leave the carcass. The hawks bones are like any other bird, they have hollow bones so that they can fly. They can not lift very much and fly away with it. They don't have the body mass to do it. If your chicken is gone, it's much more likely that a coyote did it or something like fox or bob cat.
The Red tailed hawk, the most common hawk in the US max weight is 45oz (less than 3lbs). The Cooper's Hawk, the most common chicken killer (hence the nickname Chicken Hawk), maxes out the scales at less than a pound. These hawks kill adult birds in place and may drag them a short distance and eat their prey starting at the neck usually. While they can pick up a chick, they absolutely can't pick up an adult chicken.
Regardless of their ability to pick up an adult chicken, they are deadly predators.
Im sorry, but even a very large red tailed hawk could never lift more than its own body weight, rabbit to chihuahuas sized animals, certainly not a child, they just dont have the wing span to create that kind of lift.
An Eagle, could take a very small child, but not a hawk.