Where have Sikhs established communities and attracted converts outside India?
I find it interesting that your question focuses on “where” instead of on “why” Sikhs have established communities and attracted converts outside India in its most modern stage of development. It is also interesting that you ask nothing about the guru-focused ideas behind the religion. Still, I will answer your question about “where” in the meat of my answer and then talk about why in the conclusion.
It must first be said Sikhism is not a very widespread religion in some ways. Three fourths of the Sikhs still live in Punjab. There they account for over half of the population; however, where world religions are concerned, Sikhs make up less than one half of one percent of the population of the planet. Even in India, Sikhs make up less than five percent of the Indian population.
This being said, Sikhs have established major communities in Canada where there was a vast migration of people practicing Sikhism in the 1800s. Why did they go there? Well, the British tried to colonize India and because North America was also colonized, they were welcomed. Simple as that. In short, these communities are still there mostly in Vancouver, Surrey, and Brampton (which are parts of both British Columbia and Ontario). This is evidenced by many temples, publications, radio programs, festivals, and marketplaces that cater to Sikhs as a whole.
To a lesser extent, Sikhs also participated in a minor migration to Africa, the Middle East, Asia, Britain, the United States, and Australia. The reason for entrance into these places was to help with work that was needed in those areas. In the case of the United States, because of the religious freedom afforded to US citizens, a large group still inhabits the west coast (evidenced by the same examples above in Canada). Further, tiny communities of Sikhs also inhabit many other countries, but they are few and far between.
In conclusion, the actual answer of “why” this all happened has a lot to do with British occupation and colonization of India. In reality, this was the true instrument that allowed Sikhism to spread beyond India’s borders. It makes perfect sense that many Sikhs migrated to Canada (and the United States) as a result.
I am happy to give you a little bit different take on reasoning behind where people practicing Sikhism migrated. It should be asked of Sikhism, why go beyond India? Well, at one point many gurus of Sikhism created apostles whose main goal was the same goal of any apostle: to "go out" and to proclaim the Sikhism religion to the world. In short, Sikhs migrated mostly to Canada during the more modern stages of the religion's development.
There are quite a few established communities (a few of them quite major) in the country of Canada in North America because of a great migration of Sikhs during the 1800s. North America (whether one is speaking of Canada or the United States) is known for its freedom of religion, so those practicing Sikhism felt safe going there. Now they are found mostly in British Columbia and Ontario (more specifically in Vancouver, Surrey, and Brampton). The proof of this can be provided by the number of Sikh temples, Sikh magazines and newspapers, Sikh radio stations, Sikh festivals, and Sikh markets that cater to its participants.
Sikhs didn't only migrate to North America. To a lesser extent, Sikhs also migrated to Australia, Britain, Asia, the Middle East, and Africa. The reason for entrance was to provide work that was needed in the labor force in those countries. Specifically in the US, there is quite a large community in California. Again, festivals and markets and publications and temples are evidence this fact. There are also other small communities of Sikhs in many other countries as well, but their presence does not make up any significant part of the population.