Can a black hole reach a limit where it can no longer attract more matter? If so, what happens with that black hole? Does the black hole die? Does the black hole decrease its size?

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    $\begingroup$ Note, that a black hole is not a cosmic vacuum cleaner, sucking in everything around. It behaves just like any other object with gravity. If you suddenly switched the Sun for a black hole with the same mass, it would have absolutely no effect on the solar system (besides darkness, of course). All the planets would orbit just like they did it before, they wouldn't be "sucked in". Orbiting a black hole is no more dangerous than orbiting a star, the only danger would be if you got too close to the event horizon, but even in case of a star you would be burned if you got so close. $\endgroup$ – vsz Jan 5 '15 at 16:11

There is no known upper limit for the mass of a black hole. A black hole stops attracting matter, when there is no matter within reach. In this case the (macroscopic) black hole is assumed to evaporate by Hawking radiation over very long time scales.

The estimates for the currently (as of early 2014) known most massive black holes (ultramassive black holes) are below about 40 billion ($4\cdot 10^{10}$) solar masses. A black hole of that mass would have a Schwarzschild radius of about 780 times the distance Earth-Sun, or about 4.5 light-days.

(Hypothetical) micro black holes are assumed to be able to evaporate faster than they can accrete matter.

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    $\begingroup$ Just to add something to your answer: there is no theoretical upper limit, but they claim for an observative one arxiv.org/abs/0808.2813 It seems SuperMAssive Black Holes self-regulate to avoid to swallow/disrupt their host galaxy. According to the paper the limit is 50billion solar masses. $\endgroup$ – Py-ser Apr 1 '14 at 1:20

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