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No, they couldn't. Steemit Inc does not own the blokchain or have any exclusive rights to post content to it.

Copyright and Limited License
We may retain data, text, photographs, images, video, audio, graphics, articles, comments, software, code, scripts, and other content supplied by us, the Steem blockchain or our licensors, which we call “Steemit Content.” Steemit Content is protected by intellectual property laws, including copyright and other proprietary rights of the United States and foreign countries. Except as explicitly stated in this Agreement, we do not grant any express or implied rights to use Steemit Content.

You are granted a limited, non-exclusive, non-transferable, and non-sublicensable license to access and use the Service and Steemit Content for your personal use. You retain ownership of and responsibility for Content you create or own ("Your Content"). If you're posting anything you did not create yourself or do not own the rights to, you agree that you are responsible for any Content you post; that you will only submit Content that you have the right to post; and that you will fully comply with any third-party licenses relating to Content you post.

ref: https://steemit.com/tos.html
seems Hive just copied the ToS as well: https://hive.blog/tos.html

Did HIVE used any Steemit's content (except what is already on blockchain, but they have option to delete the posts on HIVE)? I didn't saw any Steemit Inc. logos or anything else that might be protected. Steem as blockchain and condenser (frontend) are both opensource.

So people who write posts on SteemPeak could sue Steemit?

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