Say your download of 17gb application is interrupted and can't continue since you are out of space.
Knowing the application name, where can you look to find parts of what has already been downloaded so you can remove it?
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The temporary location that stores downloading files varies between computers. Here's how to find it:
storeagentfor 10.9 and below)
Open Files and Portstab, and scroll to the bottom
com.apple.appstorefrom the beginning, up to and including
open [paste path here]and hit return
Here's another way to find the Mac App Store downloads folder by enabling the debug menu:
defaults write com.apple.appstore ShowDebugMenu -bool true
Downloads, finished or not, will be in your Downloads folder in your User Directory. Unless you have specified that Safari save them somewhere else: bad idea. Ceetainly not to the desktop, as so many people think.
In the General pane of Safari preferences, you will find the setting for what folder to save to ... and in answer to your other question, you can choose whether Safari is to remove incomplete downloads: manually, never, or when successfully downloaded.
The option to Open "safe" files after downloading is way unnecessary, uncheck that only if you're experienced with security measures.
BUT, I think you're confused about downloading vs. installing. Two separate processes. Downloaded filed or zips or disk images can sit there forever. If you're asking how to fully uninstall an installed application, please ask a new question.
There is a very simple method to find downloaded .dmg files, when you wish to clean up or reuse or archive some .dmg file. This applies not only to App Store downloaded .dmg's but also to many other software downloaded using a .dmg file.
Above method is straightforward and requires nothing else than ordinary Finder functionality.
BTW, the involved folders store these files only temporary. If your only motivation is to get rid of a large downloaded file, then a restart suffices to clean out these files.
Run in Terminal to open the folder in Finder: