Why don't baby black holes give off a lot of Hawking radiation and vanish before having the chance to grow? Is it because they eat more than they eject? Or something else?
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I mean black holes which have just started forming from stellar collapse. Should had mentioned this.
Edit 2 -----
When you have a ball of neutrons which is compressed to the maximum extent physically possible during stellar collapse, the spatial curvature would be maximum at the center and would decrease as we travel away from it. However even at this point nowhere is the curvature enough to prevent light escaping.
Now somewhere between this point to the formation of singularity I suppose the 'light trapping' curvature would develop at the center and then expand outwards. So that should mean that the event horizon grows from zero to its final size in a non-zero amount of time. Even inside a black hole as far as I know the curvature decreases outwards. By this logic the Hawking radiation should start off as soon as the EH develops and should counter if not stop the growth of the black hole.
 A: There are lots of "black hole lifespan calculators" on the internet. This one by Viktor T. Toth seems to be particular comprehensive. A black hole with the same mass as our sun would take at least $2 \times 10^{67}$ years to evaporate due to Hawking radiation. This lifetime goes up with the cube of the black hole's mass. And we expect black holes that form from stellar collapse to be at least as massive as our sun, and probably several times as massive. As Toth says:

The lifetime of a one solar mass black hole, therefore, is calculated as more than 57 orders of magnitude longer than the present age of the universe. But that does not take into account the fact that such a black hole is colder than the cosmic microwave background radiation bathing it. Therefore, whatever little energy it radiates, it actually receives more in the form of heat from the cosmos. So rather than shrinking, it would continue to grow. Indeed, any black hole with a mass greater than about 0.75% of the Earth's mass is colder than the cosmic background, and thus its mass increases for now. As the universe expands and cools, however, eventually the black hole may begin to lose mass-energy through Hawking radiation.

A: I would add to gandalf61's answer, that Hawking radiation is seen from the point of view of an exterior observer, but an exterior observer does not see a black hole form from a collapsing star. He sees a "frozen star" in which time "stops" and the event horizon does not form until the infinite future.
