A black hole has a finite mass. This is generally the mass of the star that collapsed to form it.I am assuming that a black hole has an infinite mass in any direction, from a direct line from any observer.
It can of course increase in mass over time by objects crashing into it. But, that can happen to a star as well. In any case, the mass remains finite.So the mass doesn't increase over time, and if it's the same mass of the star that created it, how does it have an event horizon or the same gravitational "footprint" as the star that created it?