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First a disclaimer:
My degree dealt mainly with Britsh colonisation, and i'm much more comfortable in that area than in dealing with french and spanish styles:
But there are some key words (ideas) you should pay attention to.
All colonising powers have ideas or values they want to see reflrcted in their colonies. Of course, since this happened under colonial conditions the values were usually adopted under duress.
The idea was to "civilise" peoples that europeans considered poor, backwards and inferior in asia, africa and latin america.
At least that was the spin put on it for general consumption.
In reality, colonisation was about extracting resources and building european economies, but while you did this you still had to maintain control and look after the territories you had acquired.
and each european power had a system, and a theory for colonial rule.
Spain focused a great deal on converting the peoples in their latin american empire to christianity. This is because f Queen Isabella's commitent to her catholic faith. While others concerned themselves with the potential raches of the new world, Isabella worried about the heathen indians and their souls. The result? an early penetration by the catholic church, and the establishment of missions in all of Spain's territories. The results of this can stilll be seen in the modern USA - Los Angeles, Santa Barbara, San Diego, etc., all started as catholic missions.
the church brought with it culture - music, literature, and academics, in the form of Univesities, and to this day, the oldest UNiversities in the western hemisphere are in Latin America, e.g. the University of Cordoba, etablished more than a century before Harvard.
But while the church "civilised" Latin America, the Spanish were poor adminstrators. The audencia system was far too bulky to rule the continent effectively. Also, the Spainish sysem of ruling their empire was not flexible - all major decisions were made in Spain, hundreds of thousands of miles away. When an official wrote for advice in the audencia of nueva espana (mexico honduras etc.,) the letter didn't reach Spain for four months! By that time, the crisis was over. But officials had no authority to take initiative, and therefore could not govern properly.
For France, the key word is always "assimilation". The french did not aim to simply to convert people to christianity. The aim was to export France - the culture, the food and the language. Therefore, the french dealt with their colonial subjects differently. They did their best make sure their colonies became outposts of france, educating their subjects and encouragin them to think of themselves as french but this was greatly expensive.
As for england - the british were always practical in their empire. therefore they allowed limited self -governance in some places Canada and Australia, local assemblies made up of white settlers in others, such as South africa and kenya, and direct rule in other places, such as india. Of course these decisions were racially motivated. The british did not try to export thier culture, but rather adopted specific aspects of it to help in the running of the empire, for example their british education system. Most commonwealth countries have an education system very similar to great britain. But the idea that colonists were "british" was not encouraged. The result was the development of strong national feeling in each colony, but not necessarily a dedication to the empire. Such sentiments eventually led to the American revoultution. Americans saw themselves as americans not british subjects and fought for their independence.