What is a black hole in the sky and how does it formed?

There exists variant theories for the existence of Black Holes; one hypothesis has Black Holes being created from the collapsed stellar core of larger than three solar masses, while another has black holes predating stars and forming upon the instance of the Big Bang. In fact, the concept of a star growing or shrinking has little to do with gravitational accretion. So if a Black Hole is just a converted state of stellar evolution, then should we expect that the Black Hole size should be dependent on the amount of material being attracted and annihilated upon its Event Horizon? Per the current consensus, there is not a relevant relationship between the observable size of the accumulated bulge about the Black Hole and the size of the Black Hole itself.

And considering the Black Hole radiation jets act as the safety valve for the reactions within a Black Hole, one might speculate that, like a star, the size of the Black Hole has more to do with its internal reactions and less to do with the matter being converted upon its Event Horizon. Still another such theory has their formations predating galaxies and or even predating normal matter itself, existing unto the moment of the Big Bang itself (i.e. unfolding of SpaceTime into a traditional fourth dimensional condition).