wall mount modular unit  

Do you
really mean that there is no structure -- a row of studs, typically -- behind your (gypsum board ?) partition ? A pass with a magnetic stud finder would reveal the screws or nails used to fasten the wallboard to the studs -- or a more sophisticated finder would located any solid objects there, no matter where or how attached.
A rap with the knuckles will usually locate such members roughly, with a less hollow or reverberating sound produced where the rapping locates a stud.
I apologize if you have already been this route. It's just that I've never encountered a wall with no wood or metal supporting the surface material. . .

A rap with the knuckles give...
A rap with the knuckles give s different sounds, yeah. So do I screw the frame into the bits that sound less hollow?

Unless
you live in a caravan or an igloo, the vertical studs will be 16" / 400mm apart..find one, and you're away. ..

Walls in my NYC apartment...
Walls in my NYC apartment are about 100 years worth of plaster, directly over brick, not a stud to me found anywhere. Talk about a pain in the ass to attach things to. Sure you can drill through to the brick, but by the time you get there, you're bound to have destroyed a good sized portion of the surrounding plaster.

I'm
talking about what has already been described as a 'hollow partition wall' in a UK property.
Far be it from me to talk about walls worldwide.

molly bolt
for fixing to hollow walls
http://en.wikipedia.org/wiki/Molly_bolt
http://en.wikipedia.org/wiki/Molly_bolt