I always found it strange that the Morphos website Overview section doesn't use the "Amiga" name, but rather states:
"Just-in-Time compiler that emulates the 68k family of processors and thereby allows to transparently execute legacy applications developed for the Commodore Ax00 series of computers."
I figured it had something to do with legal/trademark issues with Amiga Inc., but now I find that they're using it in a more obscure place -- only under their GUI Toolkit section:
"Constant development and continued support from users and programmers over the past years have made MUI by far the most successfull available GUI toolkit for the Amiga platform."
--- and without any reference to trademarks at all. So perhaps their reticence to use the Amiga term has some other motivation.
