How do I assign an FBX model including submeshes to a game object at runtime?

I am new to Unity and this is the first hurdle I have stumbled over.

I have a Prefab which has a C# script component attached. A field on the attached script defines the index (or asset name) of the mesh that should be associated with this GameObject at runtime. That mesh is then assigned to the "MeshFilter.Mesh" component on the same object and is ready to render.

Now the script I am using works absolutely fine for imported FBX models which contain only a single object, however it seems to fall over when I try to do the same thing with a more complicated FBX which contains multiple objects(or submeshes?) in the same file.

It appears that: "Mesh tempMesh = (Mesh)Resources.Load (assetName, typeof(Mesh));"

...cannot load more that the first object in the file. When debugging the script I can see the name of the first object inside the FBX, and only that object is rendered to the screen.

So my question is, what am I doing wrong?

How am I meant to dynamically load an ENTIRE FBX file and render it, as if it where dragged and dropped from the project asset explorer?