How did World War I change control of Naoero?

Prior to World War I, Naoero (then known as Nauru) was under German administration as part of its Marshall Islands protectorate. With the onset of World War I, a small Australian force occupied the island and removed most German nationals.1

Following the war, in 1920, Naoero became a mandated territory under the League of Nations. While Australia, Britain, and New Zealand were collectively named as the responsible authorities, the actual administration of the island remained in Australian hands. Additionally, the island's phosphate industry was transferred to the British Phosphate Commission, a joint enterprise of the three nations.1