How can a black hole grow if time stops at its event horizon?

From the perspective of the observable universe, it is claimed that matter about to enter the event horizon slows to a standstill and is red shifted to infinite wavelength. Time in effect stops at the event horizon. How then, from the perspective of the observable universe, can a black hole grow in size, or even exist, if the material about to enter takes all eternity to p through the event horizon?