Cockatoo medium majolica toby jug in pink body produced by Sarreguemines of Lorraine, France, circa 1915, model number 3566 2. A cockatoo is any of the 21 species of parrots belonging to the family Cacatuidae. The family has a mainly Australasian distribution, ranging from the Philippines and the eastern Indonesian islands of Wallacea to New Guinea, the Solomon Islands and Australia. Cockatoos are recognizable by the prominent crests and curved bills. Their plumage is generally less colorful than that of other parrots, being mainly white, grey or black and often with colored features in the crest, cheeks or tail. On average they are larger than other parrots.