Hence the executives/boardmembers-all-fly-to-some-island (Jersey is the one in my mind), have board meeting in the airport, sign the papers, and all fly home?

Company stays "in" Jersey, none of the humans need to live there?

That is unfortunately not how it works. Most commonly the place from which decisions are made on a day to day basis is used. This results in the country in which 50% or more of your directors reside for 183 days a year.

So if 50% or more of your directors spend 183 days per year in the UK then your Estonian based business becomes UK tax resident in the eyes of the UK.

Do not underestimate the complexity of these rules.

If the company is managed 'day by day' by a local director (for example by a company like Intertrust or Trustmoore) then the non-local board and/or shareholders can indeed flyin to have 'a meeting with extensive discussions where all decisions where made and some papers were signed'. I had a company in Singapore for some years doing this.

That does not work necessarily work in the UK anymore.