Subject: Do black holes reach a saturation point and become unstable, what happens?

I was reading Stephen Hawking's book Black Holes and Baby Universes. He states 
that some matter does escape from the Black Holes. Since this is not 
proportionate to matter that enters ... Do Black Holes fill up and if they do 
what happens?  I find it implausable that an object can infinitley draw endless 
amounts of matter without becoming saturated and not have some sort of reaction 
once reaching its saturation point. Thanks for loking at my question. Have a 
nice day.

Sheldon McKee

Re: Do black holes reach a saturation point and become unstable, what happens?