Hi Pitte86. If you have a US passport and the right to legally register an aircraft with the FAA you do not need a trust company. That is a mechanism for us "furriners" to register with the FAA...........Cash saved right there.
The things you do need to consider are dependant upon where you are resident and will be keeping your aircraft. Also, for how long.
In Europe, for example, you may keep your aircraft and fly it without any particular problems. Lots of us do that. You will, however, have to import it if you are staying for longer than a "holiday" (vacation). That involves paying VAT in the country of import. If you are not importing as a VAT-registered business you will not be able to reclaim the tax (17.5% in England and more in other EU states). Big chunk of cash. You will not be able to reclaim when you eventually repatriate (in case you were thinking about it).
If you were to move to Europe, from the US, bringing your (already owned) aircraft with you - there are allowances available for that........I think you must have owned it for a set period of time before you move here.
Useful note - The Channel Islands are not part of Europe and no VAT is payable if you live there.
DME and ADF are still required over here!