European Empires

It differed continent to continent. In places like the British Raj, Diplomatic manuevers were used to ensure loyalty, along with a handful of soldiers. There were only 50,000 troops in the raj at one point. They could afford this because they cooperated with locals to backstab other locals and share power.

in places like Canada, Brazil etc, the natives were forcibly kicked out or forced to integrate, and people immigrated there. These were much easier to maintain as it's rare for immigrants to want total separation from the homeland.

>>2608862
The Industrial revolution helped. It's estimated that in the mid-19th century, England - that small island - was producing something like a third to a half of the entire world's iron and textiles.

>>2608862
They either coopted local instutions and elites and ruled through them or slowly displaced seminomadic tribes in a sparsely populated area.

>>2608862
They had tons of local help, which SJWs always seem to forget.

The most obvious might be the Tlaxcala allying with the Spanish.

>>2608862
In much of Africa, therefore, the colonial imprint was barely noticeable. Only a thin white line of control existed. In northern Nigeria, Frederick Lugard set out to rule 10 million people with a staff of nine European administrators and a regiment of the West African Frontier Force consisting of 3,000 African troops under the command of European officers. By the late 1930s, following the amalgamation of northern and southern Nigeria into one territory in 1914, the number of colonial administrators for a population of 20 million people was still less than 400. The Sudan Political Service consisted of 140 officials ruling over 9 million people. The whole of French Equatorial Africa in the mid-1930s was run by 206 administrative officers. French West Africa, comprising eight territories with a population of 15 million, was served by only 385 colonial administrators. The whole of British tropical Africa, where 43 million people lived, was governed by 1,200 administrators. Belgium ran the Congo in 1936 with 728 administrators. Scattered across vast stretches of Africa, lone district administrators became virtually absolute rulers of their domain, functioning simultaneously as police chief, judge, tax collector, head of labour recruitment, special agent and meteorological observer. In French Africa they were known as rois de la brousse – kings of the bush. A veteran native commissioner in Southern Rhodesia remembered being told that his duties as a district officer were to: ‘Get to know your district, and your people. Keep on eye on them, collect tax if possible, but for God’s sake, don’t worry headquarters.’

>>2609317
With so few men on the ground, colonial governments relied heavily on African chiefs and other functionaries to collaborate with officials and exercise control on their behalf. The British, in particular, favoured a system of ‘indirect rule’, using African authorities to keep order, collect taxes and supply labour, that involved a minimum of staff and expense. The model for indirect rule was devised by Lugard in northern Nigeria where Fulani emirs had governed in accordance with Islamic traditions of law and discipline stretching back for centuries. Lugard posted British Residents at their courts but allowed the emirs to continue to police, tax and administer justice on their behalf much as before. Similar methods of indirect rule were adopted in Buganda, in Loziland and in other parts of Britain’s African empire.
In many cases, however, African chiefs came to constitute no more than a new class of intermediaries paid to transmit government orders. As agents of colonial rule, the role they played was far removed from their traditional position at the apex of authority, balancing many diverse interests. Some chiefs were members of old royal families carefully selected for their willingness to collaborate; others had no traditional legitimacy at all. The chefs de canton appointed by the French were effectively administrative officers chosen from the ranks of the more efficient clerks and interpreters in government service. In some cases where chiefs did not exist, as among the acephalous village societies of the Igbo of southern Nigeria, chiefdoms were invented. In other cases, ‘traditional’ chiefs were left bereft of all functions.

>>2608862
They used the power of the status quo. Keep some local leaders, create some settlements for whites to move in, and/or allow locals to enter your bureaucracy, and soon enough your subjects will be collecting your taxes and enforcing your laws by themselves. Just look at India and how many Indians simply joined the English government.

I understand your question, cause it is strange how for example the portuguese with 150 soldiers defeated in battle thousands and thousands of enemies in india and other places,

https://en.wikipedia.org/wiki/Battle_of_Cochin_(1504)

and the british did the same also the spaniards.
But they made then local alliances, that´s how they kept their empires.