> I'm fairly sure the German tax authority will claim that you have a local German branch office since you live and work there. That might be OK tax wise?

If you work from home, your office at home usually does not qualify as a company office unless you make it one. In particular, that alone would not force you to pay Gewerbesteuer to the city, which is the tax specifically addressing local presence.

However, you're touching upon a very important point: If you live in Germany and your Estonian company pays you a salary (as opposed to dividends), you will be a proper employee and your company will also have to pay social security for you, and this might complicate matters significantly. In fact, this will likely (in the German tax authorities' eyes) establish that your Estonian company partially operates in Germany (which is a much broader thing than having an actual physical branch office). This then brings you back to square 1 – your company having to file taxes in Germany, too. Someone below linked https://eidel.io/posts/estonias-e-residency-is-awesome-and-s... which seems to confirm this.

> German tax authorities will see that as an illegal dividend payment from your company.

Could you elaborate? How is this illegal if you declare taxes?