Shueisha's Weekly Shonen Jump is the largest and longest-running manga magazine in the world and Nobuhiko Horie was its editor-in-chief during the magazine's "Golden Age" from the mid-80s to early-90s. During that period circulation swelled from 2.55 million in 1982 to a robust 6.53 million by 1995. The manga titles primarily influencing Shonen Jump's popularity during this era were Dragon Ball, City Hunter, Slam Dunk, Fist of the North Star and Rurouni Kenshin.
In a recent interview, Horie, who is currently the CEO of Jump, stated that the magazine's titles live and die according to the reader survey polls. Rankings determine everything from which series receive anime adaptations, whether they appear in the front or back of the magazine and ultimately- whether they're cancelled. However, the most interesting statement from Horie was the assertion that the Jump editorial team can determine whether a series will be cancelled as soon as 3 weeks. The current practice at Jump is to give a manga title at least 10 weeks to find an audience.
Bakumon, the 2008 manga series from Tsugumi Ohba and illustrated by Takeshi Obata (the team behind Death Note), chronicles two high school students who team up to produce a manga that will get published in Weekly Shonen Jump. Many of the real-world Jump editors and staff appear in the series.
Currently, the Weekly Shonen Jump rankings in the latest 2017 issue (#43) are as follows:
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One Piece
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Kimetsu no Yaiba aka Demon Slayer: Kimetsu no Yaiba (which was just licensed for North American release by VIZ in June)
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The Promised Neverland
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Black Clover
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Dr. Stone
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Haikyuu!
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Spring Weapon No 1
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My Hero Academia (1-week hiatus)
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ROBOT × LASERBEAM
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Yuragi-sou no Yuuna-san
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Hinomaru Zumou
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Gintama
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Shudan!
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Hungry Marie
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Cross Account
All of these titles are currently available in English from VIZ Media but only the most popular series are translated and released on the VIZ app at the same time as they're released in Japan. Titles near the bottom of the list are usual several chapters behind of where the series is in Weekly Shonen Jump.
As we mentioned above, circulation during the "Golden Age" peaked around 6 million but
a recent report back in May 2017 revealed that the magazine was down around the 2 million range in the wake of the conclusion of several popular titles. However, current Jump e-i-c Hiroyuki Nakano stated that while physical sales of Jump were down, digital sales were steadily rising and offset the decline in sales of physical copies. This news led to a new round of speculation that Weekly Shonen Jump might go exclusively digital in as little as 5 years.