If energy/matter deforms spacetime in three dimensions....

[cowmoo32]

Then why do we get galaxies in (relatively) flat discs and black holes that emit radiation in a single plane?

[atyy]

Well, electric charge acts in 3D, but we can still get 2D materials like graphene.

[Naty1]

Then why do we get galaxies in (relatively) flat discs and black holes that emit radiation in a single plane?

You have assumed gravity is the unique and direct cause of such phenomena..it isn't .

Spiral galaxy formation:
http://en.wikipedia.org/wiki/Spiral_galaxies#Origin_of_the_spiral_structure

Kip Thorne: BLACK HOLES AND TIME WARPS:

black hole radiation: a spinning black hole behaves like a gyroscope...near the hole the disk
remains in the black hole equatorial plane. gas accreting into the hole from its disk makes the hole spin faster and anchors the disk.

Maybe a crude analogy is the equatorial bulge of the earth.....if gravity is symmetrical around a sphere of approximate unuiform mass density, why should such a mass "bulge"..
because of the spin of earth about its axis.