There was numerous cases of insurance claims after hull loss, and most of them are going in the same direction. Ultimate Beneficial Owner.
Then two cases. Either a corporation is advertising for selling flights - > AOC
Either they are carrying "Shareholders" or "Staff" but only to the requirements of the latest ( no advertisement or sale in between) -> NCC
The registration of the plane does not matter much, even a N registered can be on ( and shall be) on Part NCC if operating from regularly ( based, even not on the papers) from an Airport in Europe.
Example : Let's imagine that VAG is an american company, but needs to operate from germany due to historical reasons. They can have their plane registered in the USA, put them at the disposition of the German entity, and operate from there, BUT if the airframe stays more than 185 days in the year or more than 12 months within 3 years, they will have to pay VAT, AND they will have to operate under NCC.
AOC : Within EASA land, to date, anybody can do anything intra states or else, does not matter (Switzerland Not), as long as they have an EASA Part CAT certificate.
FAR 135 : They can stop from/to USA, drop pax, carry on etc.. But they cannot take NEW people within EASA. For this you need prior authorization from all states overflown and of course departure arrival . (It is exactly the same when you will fly EASA AOC to the USA, and except if you apply for a FAR 129, you are limited to a finite number of flights per year)
So who has the ultimate control ? well this is the company that hold the NCC / AOC certificate for the said operation, when it is not clear, who is paying eurocontrol charges ?
Then of course if it is still muddy, Lawyers will strip down everything to the bone in order to find a whois "accountable manager".
In the case of @Dallas, This company(USA ?) is putting a plane at the disposal of an European Company for them to use within europe for a fair amount of hours, the ONLY legal way is to file an NCC ops, and transfer the authority and crews to this company for the duration of the contract. OR for every flight seek permission.