Hello,
So some numnut at the MB dealer I purchased my newish W203 from, tightened the rear lug nuts so
tight that one sheared off yesterday whiile rotating the tires, being removed the 1st time since I
bought the car. It appears it got cracked being put on SOO tight, water got in the crack and rusted right through the bolt!
I need to remove the busted piece from the hub.

So, I'm looking at extractors, and watching a "Project farm:" video on youtube.
I need the strongest one availabler and the Snapon multispline extractors appear to be my best bet.

So the question is, a 12mm bolt which is ~ 15/32", what size extractor do I use?
Also what size drill bit?
I plan to order just the one, and not the set which is mucho $$$.
Also any further advise on removing a lug bolt stuck so tight would be greatly appreciated.
Driving on 4 lugs currently. Thanks!
If you're not familiar with "Pruject Farm", you need to be. This guy will savee you so much
trouble trying to figure out what tools actually are the best.

Multispline Screw Extractor Set, 15-Piece

then you read on side of extractor for drill sie.

Lug bolts are hardened steel, so you'll need cobalt or carbide drill bits. You might find it easier to start with a small size bit and progressively drill up to the diameter you need for the extractor. Starting with a large bit increases the chance of drilling off center, laborious drilling and snapping the bit. Cutting fluid could make it go easier.

Yes as strayborx said. You will want to drill a small holes thru the broken bolt. Then drill a larger hole using the small hole as a guide and it will be easier to drill the larger hole to whatever size extractor you use.
I would also suggest getting it red hot before you try to remove it and it should come out for you.

Hopefully you won't need heat to break it free. If the bolt was installed and over-torqued many months ago and corrosion is a concern, apply some penetrating oil several times over several days before trying to break it free. Please -- no open flames near cars and especially in garages. If you need heat use a heat gun.

Why not use a torch?
I actually have a small torch for cooking that has the flame very directed to a pinpoint.
Should provide enough heat to help, no? Has a trigger operation like a lighter. Instant on and off.

It has been suggested to me to remove the brake rotor and see if there enough meat
on the bolt to use a bolt extractor that goes around the outside of the bolt
such as this https://shop.snapon.com/product/BEXM121A
But I won't know which direction to go until it's apart.
I've also read about welding a nut on the end. But I don't have any welding equip.
or experience.

People tend to forget they have a lawn mower, gas can, paint solvents and other flammable substances sitting in their garages, and relying on one's nose to sense vapors is not reliable. Rather than a complicated set of rules that spell out when it's OK to light a match in one's garage, it's simpler just to practice "never". If you insist that open flames around cars is OK, at least back you car out and work in the open air. Just remember that nearly every fluid used in your car is a flammable petroleum derivative.