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A HostileFork 
happens when someone isn’t happy about the way a collaborative effort is being run, so they start their own competing project. They take the work of the group in a different direction...rather than working on achieving a consensus. Often they lobby for developers to assist their effort, rather than the original project from which they are derived.
Not all forks in software development are hostile. Sometimes teams are divided into groups for the purpose of investigating alternatives, with the hope that whichever team achieves the best result will end up being chosen as the main line of development. "Friendly forks" occur frequently, such as in the linux glibc vs libc libraries. 
A somewhat famous example of a HostileFork is the Ubuntu  Linux distribution. The code for Ubuntu was lifted from a well-known distribution called Debian , and drew attention and resources away from the Debian project.
I'm not sure if just building on top of another project while pursuing different goals already makes it hostile
. Moreover, if your goals are radically different than the original project, you don't really compete with it, which makes "hostility by mere existence" even more unlikely. You can have hostile advertising and general marketing, you can have malicious actions and criticism of the original project's ideals and values -- that are all hostile actions
. Even the action of actually forking the project may be hostile, but not the project as such. -- anon.