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More new things? Is there a Hive app or do I need to migrate to my computer as well?

For the moment there is no HIVE app despite the majority of the DApps built on top of the steem blockchain will migrate one day or another to the HIVE blockchain.
eSTeem, exhaust, and communities, also @runningproject, will move to the new blockchain, ok?

What you have is HIVE.io similar to Steemit.com:

You can post from there.

Your profile is this one:

https://hive.blog/@marenontherun

In the coming hours they will launch the new blockchain and you will get the ability to open your wallet with the HIVE tokens there which will be a mirroring of your current steem tokens that you have including SP (which will be called HIVE POWER), Steeem=HIVE and SBD=HBD )
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If you have time you must read this post:

https://hive.blog/communityfork/@hiveio/announcing-the-launch-of-hive-blockchain

Thanks, I read the post now and will check out Hive this afternoon. Two years and one day on Steemit, let's hope for more on Hive.