LIGO detects most massive black hole merger to date

I wonder what would happen if one black hole shot through another one at high relativistic velocity, instead of spiralling towards one another.

They would merge and produce a black hole with the sum of their momentums

Because nothing can ever leave the event horizon black holes are essentially perfectly sticky.

So, if two black holes, each with mass M, were moving at nearly the speed of light and collided head-on (resulting in a final velocity of zero), what would happen to all that momentum? Would the resulting black hole have a mass greater than 2M? If so, how and why would this occur?

I think I'm going to answer my own question by saying both momentum and energy are conserved. The momentum of the entire system was zero before and after the collision. Energy must also be conserved, and since the final object is at rest, all the kinetic energy gets converted into rest mass energy, minus what is radiated away as gravitational waves.

Correct. If you're curious about the 'essence' of what black holes are I actually just did a write-up on them which you can find here: https://photonlines.substack.com/p/an-intuitive-guide-to-bla...