Is a swimming pool analogy to building of black holes in the centers of galaxies valid? In our garden, we have a little pool to enjoy our 2 children. It is 3 meters in diameter and contains some 4 m³ of water.

For cleaning-convenience every evening I go walking some 5 or 10 rounds in the pool all in the same direction, to set up a relatively fast rotating current in the pool. As a result, all of the remaining dirt (leaves, insects and seeds) are gathered together in the middle of the pool, where they can be easily removed.

So the analogy to galaxies is as follows:


The pool represents the galaxy.     
The water represents the space-time? (or all we cannot see in a galaxy? Or the galaxy as a whole?)
The dirt represents barionic matter which is forced to be dense in
the center of the galaxy, hence building the super massive black
hole.


It is clear that it is perhaps no good idea trying to map a 3m standup pool to a 100000 lightyear galaxy, but the observation seems to be worth a thought (and I do not think that I am the first one searching for analogies in that direction).

The question now is, could this be a valid analogy to the process of building supermassive black holes as a result of rotation?
The process of an eddy gathering matter to the centre of a pool is due to the motion of water in a vortex. Roughly, if water is rotating  counterclockwise then a secondary motion will be set up, rotating clockwise about an axis parallel with the tangential motion of the water. This tends to push debris towards the centre of the vortex. (The same effect causes deposition on the inside of meanders)

Space time doesn't work like this. There is very little spinning of spacetime around a galaxy, the amount of frame dragging is very small. And spacetime doesn't follow the Navier–Stokes equations, so there is no true vortex. The debris flows with the water, where as matter travels through spacetime. Your pool has a clearly defined "up", the galaxy doesn't. 

So while the appearance is somewhat similar, the mechanism is different. Though we don't really understand the mechanism of formation and growth of supermassive black holes.