ASML make fancy printers.

TSMC and other ASML customers build the designs that let those fancy printers create transistors and then logic gates, as well as a basic library of arrangements for those logic gates (PDK). They also provide all of the raw materials and processes and physics that go into said printers.

Apple and other design customers then compile RTL using that PDK to produce a design that can be manufactured using the fab’s process steps.

The printers are A hard part but far from The hard part. If you have an ASML machine it is useless to you unless you have also figured out how to build a 3D transistor in layers. Good luck!

Apple doesn't design on ASML equipment. Apple (and other fabless companies) designs to a PDK (process design kit, basically rules about how to layout transistors and passives on the die), which is given to them by their foundry (TSMC in this case).

There's a lot of steps between circuit design on the PDK to a working high volume process; and ASML machines are only part of that.

There are a lot of steps involved in making the chips - lithography is only one of them. You have to have the supply chains set up for massive amounts of silicon, you have to have a process for doping the silicon properly, you need quality control, you need to actually build a fab to house the lithography machines, I could go on.

That ASML is not undercutting TSMC and running off on their own should be telling? There's more to a running a fab than lithography.

ASML makes tools for only a small part of the semiconductor production process. It's true that EUV lithography is the big limiting factor right now, and that it is a field dominated by one manufacturer. So it's reasonable to credit ASML "as much as" TSMC for the current dominance of their high end nodes.

Nonetheless if it was as simple as buying ASML boxes there would be more than one fab at the top of the heap, and there isn't. TSMC absolutely "contributes" to their own dominance, arguing otherwise is silly.

A couple trillion dollar valuation?

You can start here: https://www.youtube.com/results?search_query=asianometry+tsm...