I was thinking about how we say clucky chook here not broody. When we grew up my grandparents had chooks and so did we and it was always the chook pen. That seemed to encompass the coop and run. I still just call it a chook pen. Just wondered what others called there chook palaces.
I remember my grandparents best. It was a dairy farm. There were no runs just pens with perches for night time. They just had the yard where the cows wondered about. I recall how the neighbours back then would exchange a dozen eggs every now and then to mix up the blood lines and of course there were roosters about.
At home we had something similar. It did have a run but I don't recall calling it anything. Maybe pen. What I remember is my mother bought spangled hamburgs. Rare back then I think. Hatch after hatch after hatch she got nothing but roosters. Only the Italian down the road was happy with them. She never got a single pullet.