The amount of Hawking radiation emitted by a black hole does not depend on the black hole's size or surface area. According to Stephen Hawking's theory, black holes can emit radiation due to quantum effects near the event horizon. This radiation is known as Hawking radiation.
Hawking radiation is a result of virtual particle pairs being created near the event horizon. In quantum mechanics, particles and antiparticles can spontaneously appear and annihilate each other. Near a black hole's event horizon, one of these particles can fall into the black hole while the other escapes as radiation. This process occurs continuously, leading to the emission of Hawking radiation.
The rate at which Hawking radiation is emitted is inversely proportional to the mass of the black hole. As the black hole loses mass through the emission of radiation, its rate of evaporation increases. Therefore, smaller black holes emit more radiation than larger ones.
The emission of Hawking radiation is not directly related to the number of particles falling into the black hole. It is an inherent property of black holes based on quantum effects near the event horizon.
As for an upper limit, Hawking radiation is expected to continue until the black hole eventually evaporates completely. However, the time it takes for a black hole to evaporate through Hawking radiation is extremely long for astrophysical black holes. For all practical purposes, the effect of Hawking radiation on black holes is negligible unless they are extremely tiny, such as those theorized to exist in the context of certain models of quantum gravity.