Charles Talleyrand wrote:

There are lots of US registered aircraft in Europe.

And the European nations accept this? They don't force a local
registry after a residency period?

Yes, they do, at least those I know (which are admittedly few). The
trick is to have the plane owned by an US enterprize and lease it from
there. There are several enterprizes which offer this service, or it is
not too difficult to create your own.

Stefan