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[Rossagues]

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[Applejuiced]

Someone downloaded them or installed them using your apple ID.
Are you sharing Apple ID's with someone? What downloads list are they appearing at? On your iphone under appstore/updates/purchased?

 

[Rossagues]

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[eyoungren]

You say the apps keep installing, but your confusion only seems to be that they appear in the downloads list.

Are the apps actually physically installing to your phone…so that you can actually open and use them?

 

[Rossagues]

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[eyoungren]

OK. I can't explain them installing the first time. That just doesn't happen. But that aside, because they DID download and install without your permission they are included in the list and that is not something you can change short of creating an all new Apple ID.

 

[Rossagues]

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[Applejuiced]

I've contacted Apple and hopefully they can shine some light on it.

That would be what I'd do.
See if they can tell you when and on what device they were purchased on.
Once downloaded once they will always appear in the purchased list.

 

[Rossagues]

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[Cmd-Z]

Not sure it would help, but you can try hiding these apps from within the iTunes Store. From your Mac's iTunes, navigate to the iTunes Store and select "Purchased" and then select the Apps category. There you'll see a list of purchased Apps, and if these show up you might be able to hide them. If you over your cursor over the top-left corner of the app you may see the familar "x" to delete (which hides) the app. I'm not at my Mac at the moment, and the PC I'm at oddly enough does not show the "x", but the cursor arrow changes to a finger if I hover over just the right spot, allowing me to hide past purchases.

Hiding the app may prevent what you're seeing, but if not hopefully Apple can resolve this.