In a wasted spark system if the firing plug on the compression stroke requires 10,000 volts and the wasted spark coil is designed to put out 20,000 volts, is the voltage split in half. How exactly does this work at any given time?
I think you have a bit of a misunderstanding about how wasted spark systems work. In your statement, you are talking about two separate output voltages to fire separate spark plugs, yet there is only one output voltage.
A single coil will fire two separate spark plugs at the same time. The two spark plugs will be located in "companion cylinders". In a four stroke engine, this equates to one piston which is near top dead center (TDC) at the end of the compression stroke just before the power stroke. Its "companion" cylinder has its piston in the same place coming out of the exhaust stoke and entering intake stroke. There are two windings in the coil: primary and secondary. The primary winding is at input voltage (~12vdc or battery/system voltage). The secondary winding is the output voltage, usually in excess of 20k vdc (could be different depending on the application and manufacture).
The way this works is depicted in the following image:
The secondary circuit (or winding) fires one spark plug from electrode to ground strap and is then routed (in the same circuit) from ground strap to electrode. (Source 1 and image source) This is a complete circuit.
What this means is, the ignition system is a lot less complicated than what you were thinking. Only one coil per two cylinders. Only one input/output voltage per coil. All it needs is a trigger to fire it, which is usually timed from the crankshaft. NOTE: The ECU will usually send the trigger to the coil, but the timing itself comes from the crankshaft, as opposed to the distributor type ignition system which gets it's timing from the camshaft.
The coil is able to provide in excess of the spark plugs requirement. However, understanding what happens to voltage at the electrode tip is a slightly more complex affair.
What happens at each side of the air-gap in the spark plug is that the air becomes ionised, positively and negatively charged around each electrode. As the voltage increases, the polarity field increases in size until they both get so bit that they touch each other. At that point, the plug "sparks" and a blue electric arc is formed. This arc causes the voltage in the system to drop to zero.
It just so happens that I watch a semi-related video about it on youtube last night which concerns itself with Tazers but the theory is exactly the same. Take a look here.
Another version of a waste spark system , as on my trusty old BMW twin cylinder bike is one contact breaker running from the half speed twin lobe camshaft and firing two 6volt coils wired in series -only one set of points to adjust