Do Supermassive Black holes ever stop growing? Do the Supermassive Black holes at the centre of large galaxies ever stop growing? In other words, do they eventually consume their entire 'host' galaxy?. is it a case of: the more they suck in > the greater their mass > so the more they suck in, ad infinitum? If they do stop growing, what is the mechanism behind this cessation of growth please - i.o.w. do they somehow get filled up? ...(perhaps to the point where they expand again/explode?)
 A: The mechanism is called rotation. The objects of galaxy are rotating around the black hole just like earth rotates around sun and does not fall into it. At greater distances, the black hole has no different effects from those by any other object of same mass. Therefore, even if some mass falls into it (somehow), and it becomes heavier, that does not mean it will gobble more stuff. Due to increased mass, other object may come closer to it and start rotating faster but would not fall into it.
But it would eat most of anything that comes in its path and those things are usually not objects of host galaxy.
A: Black holes grow through the process of accretion i.e. using their gravitational force to pull matter (typical gaseous matter), so that it is only logical that when this mechanism is not strong enough the black holes has pretty much reached the maximal mass possible (technically it can further grow in the case an object falls directly into it due to its natural trajectory but you get the idea). 
In his paper, titled "How big can a black hole grow?", Andrew King argues that a black hole can not grow more than $5 \times10^{10}$ solar masses for the typical parameters, but can reach a maximum as height  as $2.7 \times10^{11}$ solar masses in some extreme casses.
I've heard some scientist believe that his calculations are an over simplification, but it is generally believed that that order of magnitudes is correct.  
The interesting thing is that that value does not exceed the masses of some ultramassive black holes identified in some galaxies (for e.g. the ones detected with NASA's Chandra X-ray telescope).
