Is this for the schematic symbol editor?
I’ve made a screenshot of that windwo with an approximate size of 1366 * 768 which is I think about the smallest screen which is still in somewhat wide use (maybe laptops and such). The width of the tree can be changed by dragging the vertical bar and according to my screen ruler the narrowest is around >>> 250/1366 = 0.18301610541727673.
But you can toggle the whole tree on & off with this button: 
on the left side toolbar, or with: Symbol Editor / View / [ ] Search Tree from the main menu.