What's the technical name for the part that holds
 

the front turn signal housing to the body on a 2004 Cooper S

http://www.realoem.com/bmw/enUS/

They call it a finisher, I always just called it the side T/S housing....

My mistake, its the fog lights that sits behind the bumper.

It isn't clear what you're asking about.

Do you mean the nut and screw?
http://www.realoem.com/bmw/enUS/show...diagId=63_0630

What holds the whole unit in place? It is screwed to a black round assembly.
The horn sits on top of this assembly.
What does #2 and #3 from the diagram screw into?
What holds the fog lights to the rest of the car?

Look at the diagrams here: http://motoringfile.com/howto/Fog%20Lights.PDF

This is the part it attaches to: https://www.ecstuning.com/b-genuine-...l/51647200800/

The "cup" that holds the fog light assembly is a part of the Core Support, it's not a separate piece.
That's why we were having trouble figuring out what you were referring to.

Thanks. So its called "Core Support"?

I've always called it that, or Radiator Support, but I just looked it up, RealOEM has it listed as "Front Panel".

Part #5

Attachment 141831

I had no idea until just after your posting that the whole panel from one side to the other came in one piece and that's why I was just looking for one support piece.
I didn't know how to explain it so that you guys would know exactly what I was looking for.