OK, so... it works by tracing backwards like normal, but with extra rays 
being spawned for diffuse illumination, approximately? (Just like 
specular reflection and refraction require additional rays.)

Well, that answers the main question.

Just to clarify... Are rays fired evenly in all directions? Completely 
at random? Are they set up to "avoid" the object under consideration? 
Are their directions in any way related to the direction of the ray that 
hit this surface in the first place? Does the total computed intensity 
take into account the different angles the light is illuminating the 
surface from?

You say the process traces backwards according to the max trace limit. 
(In fact, I think there might even be a parameter to change it for the 
radiosity system so it's different to the main trace.) Does POV-Ray only 
save the final intensities, or does it cache all the intermediate values 
too?

Andrew.

PS. Some graphical diagram in the help file would be really useful here. 
I /think/ I understand the overall principle now, but for a long time I 
was very confused by this feature.

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