Well no, your ISP isn't "after" anything really (Other than mass data collection to create databases and improve search options). But they can see everything you connect to, and if you are using Tor the chances of you viewing illegal content are significantly higher than just a surface web browser and if you do view illegal content, and your ISP records it you can and most likely will get caught.
The best way to become the closest thing to totally anonymous on the internet:
Use an offshore VPN with no connections back to you.
Use Tor.
Disable javascript.
Use common sense.
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