I had three of these gorgeous fellows in my backyard a couple of weeks ago. I heard them passing by, but was too slow to catch a glimpse of them as they headed toward the local park. An hour or so later, I heard them again and rushed out to see them sitting in the top of my casuarina tree and munching on its cones. I spoke to them and they muttered back at me, eventually swooping low out of the tree (as if to bid me a happy farewell) and flying off toward the bush where they live. These beautiful black fellows are much more finely constructed than the Sulphur Cresteds or the Corellas. They have long slender bodies, more like a parakeet type. Instead of the SC's broad wings, they have longer, more pointed wings which are more suited to agile flight among trees (where they live).
Yellow-tailed Blacks aren't usually seen in the town. They much prefer living in closed forest (ie. where the canopies of the trees meet overhead) where there's good cover from our numerous birds of prey (notably Wedge-tailed Eagles, White-breasted Sea Eagles and Peregrine Falcons). I've seen flocks as big as fifty or so out in the bush, but we get the occasional pair or quartet in my suburb. They come from local bushland to forage for flowers and fruits in parks and gardens. They always fly the same route out in the mornings and home in the evenings. They have a plaintive flock call that's nothing like the screech of their white cousins.
I used to think I'd like to keep cockatoos, but my experience has taught me that cockies belong in the wild, not in cages. I've watched so many of them go mad in captivity, I don't think it's worth breeding them for the pet market. Just my opinion, though. I'm sure others will disagree.