The primary function of the list of aircraft operators is to facilitate the good administration of the EU ETS and to help aircraft operators to contact the correct administering Member State. However, inclusion of the aircraft operator on the list does not presume that the aircraft operator is covered by the EU ETS. That depends on the aviation activity of each aircraft operator.
European Commission regularly updates the Prior Compliance List, which provides an overview of aircraft operators that have not yet been included in the official list of aircraft operators. Prior Compliance List is a support function to the new aircraft operators or aircraft operators that are no longer covered by the EU ETS exemptions (fx. due to an increased aviation activity), and provides aircraft operators with the info on its administering Member State. Thus, aircraft operators can prepare its monitoring plans before they officially are being allocated to its administering member state.
European Commission has elaborated an official document that provides an overview of the rules under the EU ETS, such as allocation to the administering Member State and aircraft operator's registration, etc.