They are flat due to the conservation of angular momentum. Once a black hole forms in the center, its gravity affects everything around it. Objects affected by the black hole collide with each other and cancel their momentum in all directions except for the direction of the rotation of the hole.
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All that money I spent on framing Hubble pix to put on the walls is seeming ill advised now ☹️😆
However, smaller dwarf galaxies may not have a supermassive black hole and may look more like a cloud than a disk.
I’m sure Katie can expound. 👍🏽