The Western Desert can be said to stretch from the Nullarbor in the south to the Kimberley region of Western Australia in the north , and from the Percival Lakes in the west through to the Pintupi lands in the Northern Territory . The Western Desert can be said to stretch from the Nullarbor in the south to the Kimberley in the north , and from the Percival Lakes in the west through to the Pintupi lands in the Northern Territory .