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It doesn't use your Internet connection because Home Sharing only uses your router to create an ad-hoc connection between your computers and devices, without using Internet
This is mostly correct - however be aware that internet is required for very brief authorisations of protected content played via Home Sharing across the LAN, but I suspect 99.999% of bandwidth used will be LAN based.
The OP should also however ensure that any intended playback from iTunes is made via the Computers icon on AppleTV.
If you play via Purchased sections of the top level Movies or TV Shows icons or iTunes Match if they have that, then the content will stream for the internet.
AppleTV does things in many ways these days and it can be confusing, and easy for people to access internet content vs LAN content if they don't realise.
Does the homesharing count towards my allocated internet bandwidth?
If you are getting unexpected usage costs, there is an option somewhere to send diagnostic information to Apple - I doubt it does much but some have suggested it uses excessive bandwidth so perhaps best turned off.
Also if you rent from teh internet via movies and rewatch within the 24/48 hour view period AppleTV can often redownload the whole movie increasing usage.
But I doubt !
If the internet get disconnected, the content sharing over the LAN also stops.
I agree that the idea of Apple TV is to do share the content over intranet and not over internet but why does the sharing stop when the internet goes off. Ideally, one time authentication on both itunes and apple tv should be done and then the content should be flown within the LAN and it may be doing that even, however, the experience with a turned off internet is different. Can somebody solve this puzzle with authentic answers?