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The publishing model you're suggesting isn't actually all that new. Serialised novels - novels published in newspapers or magazines, one chapter at a time - were very common back in the 19th cent...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/48457 License name: CC BY-SA 4.0 License URL: https://creativecommons.org/licenses/by-sa/4.0/
#2: Initial revision
The publishing model you're suggesting isn't actually all that new. [Serialised novels](https://en.wikipedia.org/wiki/Serial_(literature)) - novels published in newspapers or magazines, one chapter at a time - were very common back in the 19th century, starting with Charles Dickens' publication of _The Pickwick Papers_ in 19 monthly instalments between 1836-37. Novels published this way include Arthur Conan Doyle's _Sherlock Holmes_ stories, _The Three Musketeers_, _The Count of Monte Cristo_, _Uncle Tom's Cabin_, and _Anna Karenina_. With the rise of TV and radio, print media largely moved away from serialising novels, but it still happens occasionally; _Rolling Stone_ magazine serialised a draft version of _The Bonfire of the Vanities_ between 1984-85, and Stephen King experimented with publishing his unfinished novel _The Plant_ as a serialised e-book all the way back in 2000. Now, in 2019, there's an iOS/Android app called [Serialbox](https://www.serialbox.com/) that works exactly as you describe: stories are divided into "episodes" like a TV show would be, with new episodes released weekly. Serialbox seems to mostly cater for sci-fi and fantasy, and I don't know whether you'd be able to publish your specific story through them. But their very existence tells me that the answer is: **yes, there is still a market for serialised literature.** Whether these serialised works are "successful", and whether anyone would be interested in _your specific_ work, is probably a matter of opinion.