Do you mean WWI, in which case it was the Central Powers, or WWII, in which case they were known as the Axis?

In the case of WWI, the Germans had control of a number of islands in the southwest and central Pacific, as well as Nauru and Papua New Guinea (known as Kaiser Wilhelm's Land). They had a cruiser squadron that operated their early in the war, 1914-15, and this was the source of some anxiety for Australian/New Zealander Political and Military leadership before the war. I could point you to a number of sources on the subject: Peter Overlack's PhD Thesis The Imperial German Navy in the Pacific, 1900-1914 as an Instrument of Weltpolitik with special Reference to Australian operational Planning and his War and Society article "Australian Defence Awareness and German Naval Planning in the Pacific, 1900-1914"; Jürgen Tampke's edited collection Ruthless Warfare: German Military Planning and Surveillance in the Australia – New Zealand Region before the Great War: Documents; John Moses and Christopher Pugsley's edited work The German Empire and Britain’s Pacific Dominions 1871-1919: Essays on the Role of Australia and New Zealand in World Politics in the Age of Imperialism; and the Central European History article "Admirals versus Generals: The War Aims of the Imperial German Navy, 1914-1918" by Holger H. Herwig.

The aim of Kaiser Wilhelm and of the German Navy was that continental hegemony gained through victory over the Entente would provide a springboard for power-projection via the High Seas Fleet. Michael Epkenhans' work on the Imperial Navy, and Fritz Fischer's seminal work on German War Aims Griff nach der Weltmacht, are especially useful here. The end goal seems roughly to have been to accumulate spheres of influence in the Southern Hemisphere via continued economic penetration of South American markets, which had already seen Germany 'lightly brush elbows' so to speak with the Americans; steady growth of the German presence in the Ottoman Empire; the creation of a central African empire, Mittelafrika, by annexing Belgian Congo and some French territories; and by use of Germany's territorial possessions in the Pacific ocean and China (ie Kiachow, Shantung). I'm unaware that the Central Powers had any plans for Canada, but the Germans did have a sabotage/terrorism network in the United States, and some of their actions like the Vanceboro Bridge Bombing in 1915, were perilously close to the Canadian border.

In the event of a German victory on the Continent, especially with a settlement mirroring Bethmann-Hollweg's September Programme, Britain would be in a worse position than in 1940, as the U-Boat threat would have been enhanced, but the threat of the German Surface Fleet would be even greater. Combined with the potential Central Powers threat to the Suez Canal via the Ottoman Empire and Egypt, Australia and New Zealand could find themselves in a situation very similar to that of 1942, when Churchill essentially 'wrote them off' as a loss, to focus on North Africa and the defense of India.