Italy/Ireland double taxation treaty...
Italy - Tax Treaty
2. The term "permanent establishment" shall include especially:
1.a place of management;
2.a branch;
3.an office;
4.a factory;
5.a workshop;
6.a mine, a quarry or other place of extraction of natural resources;
7.a building site or construction of assembly project which exists for more than twelve months.
4. A person acting in a Contracting State on behalf of an enterprise of the other Contracting State-other than an agent of an independent status to whom paragraph 5 applies-shall be deemed to be a permanent establishment in the first-mentioned State if he has, and habitually exercises in that State, an authority to conclude contracts in the name of the enterprise, unless his activities are limited to the purchase of goods or merchandise for the enterprise.
So presumably you can't buy a ticket at the check in desk?