Massive black holes

If time stops at a singularity, how can massive black holes grow?

 
Singularity

Astrophysics. A point in space-time at which gravitational forces cause matter to have infinite density and infinitesimal volume, and space and time to become infinitely distorted.

 
I don't think time stops, it just becomes infinitely distorted.

If a black hole has infinite density and infinitesimal volume, does it grow or is it its event horizon that grows? Its event horizon would continue to grow by the black hole's consumption of additional matter increasing its gravitational strength.

Theoretically, of course.

Time only slows from the perspective of the object falling into the black hole. From an outside observer's perspective, the object falls into the black hole at the same speed you would expect for any other object.