Togo: // Would a singularity not produce a dome of influence on the matter around it rather than a 2d flat plane? //
I think in the end I answered this question already. You are right that a perfectly spherical, static black hole would attract matter in all directions, but...
// ... this Black hole is rotating, so what you are seeing is a disc [of material spinning around the black hole]. //
It's not difficult to introduce a rotation. All it takes is for material to fall to the centre with even the slightly hint of angular momentum, and then because that is conserved, as the black hole gets smaller and smaller it will spin faster and faster. Imagine, for example, rolling a coin on the table. Doesn't take much for it to end up moving in ever-decreasing circles. That makes a particular disc "preferred" for the material to gather around, rather than just falling in from all directions.
Hope that helps!