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?

Energy and momentum are always conserved in EVERY physical process. We can distinguish three types of collisions: “sticky” ones, in which the kinetic energy decreases (typically, it is converted into heat); “explosive” ones, where the kinetic energy increases; and elastic ones, in which the kinetic energy is conserved. Since the total energy (rest plus kinetic) is always conserved, it follows that rest energy (and hence also mass) increases in a sticky collision, decreases in an explosive collision, and is unchanged in an elastic collision. The resulting black hole in other words would have way more of a mass than 2M since you're talking about a 'sticky' collision in the above instance. You can see an example of why this is in Griffiths' text (Introduction to Elementary Particles (which I highly recommend)) -- page 101 contains a great example of what happens to the mass of particles in 'sticky' collisions: https://www.hlevkin.com/hlevkin/90MathPhysBioBooks/Physics/Q...