1. 3 Manga that start near the same time and become the most popular, as well as an anime adaptation
2. for them to hold up well in their beginning and in the future
3. for them to continue for a long time, (around 10 years or more, even anime things count as content. (the Bleach anime counts even though the manga is finished))
its what made the Big 3 the big 3, and if these conditions aren't met then the Big 3 is still Bleach, Naruto and One Piece...