Why do 3d spheres and gravity tend to rotating discs on one plane? Whether is it our solar system or a whole galaxy, there is usually a massive object (star or black hole) at the centre with gas and objects rotating around it. 
The gravitational effect of the star/black hole extends uniformly (more or less) in every direction in 3d. Why does matter tend towards a single plane?
Furthermore, what happens to matter that approaches after the "disc" is formed when it is pulled in from anywhere off the plane, why does it join the plane rather than forming another plane?
I suspect angular momentum has something to do with it, but would appreciate a "pop science" explanation.
Many thanks
Andrew
 A: You're right, it's basically because of angular momentum. In essence, if you start with a self-gravitating cloud of material or collection of particles with a mean angular momentum (which needn't be particularly large), then the material smears itself out perpendicular along the plane of rotation (perpendicular to the axis of rotation). The individual motions perpendicular to the plane roughly cancel out through assorted interactions. But, at least on average, the material is all orbiting in roughly the same direction, so that component is preserved. In even broader terms, the evolution allows energy to be lost (through collisions, heating, etc.) but losing angular momentum is much more difficult. 
If it were the other way round (i.e. losing energy is difficult, angular momentum easy) then we might expect spherical clouds. For example, in dark matter halos, it's very difficult to lose energy because dark matter cannot radiate energy away, so they remain diffuse and more broadly distributed. i.e. they don't collapse into discs. Giant ellipticals are thought to be the remnants of mergers between massive galaxies and the random orientations of the input angular momenta mean that the remnant has a smaller angular momentum relative to its energy.
Beware of placing too much importance on the central object, though. In the case of, say, an accretion disc around a compact object (white dwarf, neutron star or black hole), the central object totally dominates the behaviour of the orbiting material. In the Solar System, the central object (the Sun) mostly dominates the orbital behaviour but clearly there are smaller systems where other objects rule, like planets over their moons. In the Milky Way, the central black hole actually only dominates over a small region in the centre. Our orbit is determined by the black hole and all the stars, gas and dark matter inside our orbit. It doesn't affect the description above but I thought it was worth saying.
It'd be really great if there was an animation of the "smearing out" of a sphericalish cloud into an accretion disc but I couldn't find one...
A: It's not true that everything tends towards a single plane.
A counterexample are the dark matter halos of galaxies : See for instance http://news.bbc.co.uk/2/hi/8444038.stm .
A: The way I look at this is to wonder what would happen if things weren't in the same plane.


*

*The obvious issue is collisions - space may be quite empty but if you have a large amount of dust orbiting in different planes there will be collisions

*Gravitational forces - more likely than collisions, when bodies come near they affect each other. In a plane, the forces will also be in the plane; where two bodies are in different planes the forces will alter the orbits. This leads to two simple steady states - objects ending up in the same plane, or one being flung out of the system

*Angular momentum - even if the initial aggregate movement of all the particles in a dust cloud is small, by the time they have fallen towards each other they would have built up spin, as angular momentum needs to be conserved. Having particles orbiting in different planes or directions will cancel out momentum, so the simplest outcome is for spin to happen in the same direction

*Drag - energy losses occur, but these are least if all objects are orbiting together

A: On the level of a star, it spins during its life so "everything" around it will be on the same plane it spins on.  Even a comet flying by will be pulled toward the objects of mass which will be on the same plane as the spinning star in the center.  So eventually everything will be on a similar plane.
