If you are BASED in Italy and register in Ireland or Estonia I'm pretty much sure you are breaking the law, EU or not.
On top of taking care of this, I also make sure I do not "awaken sleeping dogs": * every single bit of fiscal administration both here and there is perfectly in order * even if 100% legal and in order, I avoid creating visible links between myself and my company (bank accounts, ownership declaration, ...). (I make a small exception here, but I'm usually not very keen on it...)
You will find a lot more information on this subject area in the double taxation treaties between individual EU member states.
The general principle is very simple: the fiscal residence of your company is where your company's main and real activities are, as evidenced by facts. Unless you are a big multinational of course, in which case all these rules go overboard by using the tax avoidance loopholes and custom fiscal rulings.
1) "Company in foreign country does not really mean lower taxes." It does in my case, and in plenty of others. 15% instead of 33.99% corporate income tax for example. Legally.
2) "You still tax your income in country of residence." One's personal income is indeed taxed in one's country of fiscal residence (except for the exotic regime US citizens are subject to). My company's income is taxed in its country of residence.
3) "But it often means lower administration." Not always. Luckily true in my case.
To be more specific, such structure would not be illegal, but you would have to deal with double the amount of bureaucracy and you would pay the same taxes.
How would you expect this to be remotely legal ?
Sure, there are plenty of people doing that, just as there are companies registered in the Cayman or Gibraltar, or people having secret Swiss bank accounts.
If you pay taxes (in Italy, say) on the income from your company, wherever it happens to be.
I get the impression that it's all something of a legal gray area. It'd be a lot simpler if people could easily have companies in their own countries.
I'm all for paying one's fair share of taxes on income in the country you live in. What I intensely dislike about the laws in Italy surrounding companies is that there are all kinds of expenses that have to be paid even if you are losing money.
Its mainly about which country's employment laws apply.
The company is a separate legal entity.
The company pays corporation tax in the country where the company is registered, you pay income tax in the country you live, and then there is also vat.