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Offshore company + self employed in EU. How to structure?

It's improbable that for such a small-scale structure, they would start cross-border tax investigations, which is expensive.

You're probably right.

It's important to note that an additional benefit of operating as a branch office is that your identity will not be reported as UBO in this jurisdiction (or EU UBO register) since branch offices are exempt from UBO reporting, so consequently information about them shouldn't be reported between authorities as smoothly compared to companies.

That's a nice cherry on top.
 
The sanction of the GAAR lies in denying of a tax advantage because it would go against the object or purpose of the applicable tax law.
There is very little court practice on that matter, but I imagine it will be less applicable cross-border. No jurisdiction would be interested in reducing its tax base or the amount of taxes it gets, so there is an ingrained conflict. Moreover, no jurisdiction is interested in contributing resources to reduce its tax base so one party never benefits from the co-operation.
ATAD makes it clear, however, that taxpayers should have the “right to choose the most tax-efficient structure” for their commercial affairs, limited only by the requirement that they not be “non-genuine”.