I think you need some explanations: (note that I don't know the details of the implementation so I may be wrong, though I think what i say is roughly how it works)
First see this:
[img]http://www.trolltech.com/images/embstack.png\" border=\"0\" class=\"linked-image\" /]
Qt is a set of widget (ie boxes etc)
Qt/X11 and Qt/Embedded are 2 porting layers that gives the basic functions (maybe a drawline function for instance) that are then used to implement qt, using either the X11 library for the first, or directly the framebuffer ie the hardware in the second case.
X/qt is an implementation of the X server that uses the drawing functions of the Qt/embedded layer (At least I suppose)
Pdaxrom uses an X server that uses the the hardware drawing functions.
Pdaxrom has the Qt library built on top of qt/X11.
So in theory applications using qt work on both X and qtopia, (though there may be some little problem with version, little difference etc....) and in practice kdepimpi runs on 3 platforms with almost the same code.
Next there is qtopia, which is a desktop environnement built on top of the Qt layer, this provides the desktop the bar some methods for applications to communicate etc..
So if a qtopia application uses this api in order to run in pdaxrom it also needs the qtopia layer (running on top of qt/qt/X11)