So, there's this idea, which you already know: Define the layout of your UI by creating a tree of panels. The leaf nodes on the tree are what we used to call 'controls' way back in the day-- the things that the user interacts with, radio buttons and listboxes and such. The internal nodes are mostly concerned with layout; this kind of panel stacks its child panels vertically, that kind puts its children into a grid, etc.
It's COMMON. Most of the UI-generating systems I've seen in the past twenty years are implementations of this, and the ones that aren't borrow from it.
What's the word for this idea?
EDIT: I'm looking for a word, or a phrase, for the pattern I'm describing. It's a big, high-level pattern, and it's become nearly universal. AWT, HTML forms with the controls in table cells, Swing, XAML, Android, and ASP.NET all use it or borrow from it. There's an idea here, on the same level as concepts like "windowing system" or "mesh network." What do we call it?
I suspect that the real answer is, "there's no consensus on a name for it yet." Which would, itself, be really interesting.