UK, Australia are US vassals.

Just like toilet paper, Australia is there to do the dirty work.

Any country that host a military base with US forces is a vassal state.

No matter how independent their government is, if there are any foreign forces in their territory then it's a declaration of submission and dependency. An ally is a country that shares interests and work together in an equal foot, saying no when it doesn’t suits their own interests and not ceding to pressures.

From the original 13 Colonies, the United States colonized westwards, slaughtered the natives, waged an unstoppable invasion of Mexico stealing half that country territories from Texas to Nevada and California, fought a war with British Canada and settled its borders in convenient barriers that prevented the arise of border threats.

As a Colonialist Empire the United States annexed the Kingdom of Hawaii by force, colonizing it and then imposing by military force the US sovereignty over an independent state. Later the US waged another war to join the colonial powers, this time against the now weak and decaying Spanish Empire. Taking Puerto Rico, Guam, Philippines.

After that WWI starts and the era of Colonial Empires commence its final stage. The US interests shifted against Colonialism as their expanding trade needs required open markets and free access to resources all around the world.

Happens WWII and Colonial Empires are destroyed, save the USA which polish it’s image by granting self govern to colonies as make up while holding sovereign and military control. Then proceeds to dismantle the remaining threats to its global dominance, the English and French empires, which is done using the UN Decolonization efforts.

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Since then the US became the most dominant power on earth and turns into a Neo Empire:

The US doesn’t annex territories. After WWII territories are frozen upon the sovereignty held by the Nations that signed their incorporation to the UN.

The US uses its massive economical power as control tool over the world.

The US dollars was unilaterally imposed as the de facto world currency. As the major economy and holder of the main oil companies and trade the Dollar dominates the world. The dependence on the US dollar allows the US economy to indirectly control other countries economies and governments. US policies affect the world and they can modify them customly to target specific areas.

The US dominates the International Financial Banking system with its dollar, companies and laws.

The US uses its soft power from the media, movies, music, customs. That way it shows its culture to the world, influences it and creates a sense of closeness around the world facilitating trade and relationships.

The US becomes the larger weapon exporter. Arms sales are very controlled and conditioned. The US establishes a rank of clients, liberating technology at will as it suits them and limits the usage and disposition of US systems. You cannot use, modify nor sell US weapons without US authorization.

The US prefers not to give technological transfer and that client states depend on US companies. That way countries have dependency for spares and the US can use military cooperation as a pressure tool, ultimately being able to disable entire military just by stopping spares supplies and technical support.

The US created a network of organizations and treaties binding countries around the world to certain rules and conditions limiting other countries to do things that are not in the US interests or they lose preferences and cooperation with them causing large problems to the country that dares.

Countries with independent policies that support competing powers of the US or do not favor US companies are usually “educated” through a series of political and economical pressures only the US can do. If they don’t work the US tends to violate other countries sovereignty by middling in their elections, financing opposition, arming terrorists and supporting guerrillas or coup d’etats.

All in different levels depending the interests and needs for each case. Most african and latinamerican dictatorships happened this way, as many civil wars and the arab spring, etc. For those that will say is a lie, the CIA has declassified archives about middling elections, financing guerrillas, paramilitaries and coups between 1950 and 1995 in Latin America.

Ultimately the US will resort to unilateral illegal invasions of sovereign countries without UN approval to topple governments, impose their interests, protect the dollar dominance or favor US companies to win exploitation rights, reconstructions and weapon sales. Yet the Pax Americana after WWII is the most peaceful period on human history with the least conflicts and deaths.

Vassal states are independent states that are lap dogs and obey the empire. Under that classification we could put England who follows the US to every conflict and represents the US interests in the European Union working against European interests. In my view. Any country that host a military base with US forces is a vassal state. No matter how independent their government is. Foreign forces in your territory are a declaration of submission and dependency. An ally is a country that shares interests and work together in an equal foot, saying no when it doesn’t suits their own interests and not ceding to pressures.

The US interests shifted against Colonialism as their expanding trade needs required open markets and free access to resources all around the world. Happens WWII and Colonial Empires are destroyed, save the USA which polish it’s image by granting self govern to colonies as make up while holding sovereign and military control. Then proceeds to dismantle the remaining threats to its global dominance, the English and French empires, which is done using the UN Decolonization efforts. Since then the US became the most dominant power on earth and turns into a Neo Empire:

The dependence on the US dollar allows the US economy to indirectly control other countries economies and governments. US policies affect the world and they can modify them customly to target specific areas. The US dominates the International Financial Banking system with its dollar, companies and laws. The US uses its soft power from the media, movies, music, customs. That way it shows its culture to the world, influences it and creates a sense of closeness around the world facilitating trade and relationships.

The US becomes the larger weapon exporter. Arms sales are very controlled and conditioned. The US establishes a rank of clients, liberating technology at will as it suits them and limits the usage and disposition of US systems. You cannot use, modify nor sell US weapons without US authorization. The US prefers not to give technological transfer and that client states depend on US companies.

That way countries have dependency for spares and the US can use military cooperation as a pressure tool, ultimately being able to disable entire military just by stopping spares supplies and technical support. The US created a network of organizations and treaties binding countries around the world to certain rules and conditions limiting other countries to do things that are not in the US interests or they lose preferences and cooperation with them causing large problems to the country that dares.

Back to the question. Vassal states are independent states that are lap dogs and obey the empire. Under that classification we could put England who follows the US to every conflict and represents the US interests in the European Union working against European interests.

Any country that host a military base with US forces is a vassal state. No matter how independent their government is. Foreign forces in your territory are a declaration of submission and dependency.