Both of your assumptions are correct. It's really all up to your strategy. Some people like to pump out articles for easy keywords, and then suck up the traffic that EZA brings in. Others like to use articles mostly for backlinks by spreading it across the internet. Some prefer a combination of both.

If you want to know which is better, it's up to you. In my opinion, ranking the articles on your website would be more important in the long run than ranking your EZA articles (EZA would be easier to rank for in the beginning, though, which is why some people prefer backlinking EZA).

Speaking of backlinks... Do you want to backlink to your main site with ALL of your backlinking or would you backlink to specific pages within your site? Or is it a mix?

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Backlinks are important for SEO because some search engines, especially Google, will give more credit to websites that have a good number of quality backlinks, and consider those websites more relevant than others in their results pages for a search query

Your thoughts are quite correct, I have seen most of the peoples who just write the article for the purpose of getting back links only, there are others too who are just writing to bring up it to ezine but they are very less.

You are right and you can do it too. But some websites which are offering services or some products, and don't have too much text in their websites, have to write articles in other websites and promote them. But if you can write articles on your website and promote them, do it for your website instead of article directories.