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1- When will be the next release of Akamaru Jump? and what's the general look of the cover?
2- What is the little piece of paper that I find between the pages of a tankoubon?
3- Why the American versions are thicker than the Japanese despite the same amount of pages and content?
The next Akamaru Jump will be out in May. It always comes out after New Years, Golden Week (first week of May), and Bon (August). The cover looks very similar to Weekly Jump, generally featuring one series. This is the winter issue cover:
Sorry but I don't know the answer to your other two questions.