What is the recommended height of cakes when making a two-tier chocolate mud cake? Or to get a decent height, should I make (as an example) two shallow nine-inch rounds for the bottom layer and two shallow seven-inch rounds for the top layer?
As a note before the post I am more scientist than baker.
The stress you can put on a structure before it severely deforms depends on a lot of things including it's Young's modulus. These are very well understood for construction materials but I came across this paper which discussed it for various cake recipes (PDF). The recipe I found for mud cake has about 27% flour so I used values accordingly for my calculation.
If we assume that we do not want more than a 5% deformation (this may seem like a small number but my estimation is an attempt at being conservative, plus it would be at the very least noticeable) then the maximum height would be about 28 inches.
Or to put it another way, your two 9 in pans for the bottom layer and the 7 in for the top would make a delicious cake with some room left over for frosting. If you are really concerned about structure I also came across this recipe which kind of talked about that as well (much more so from a baking perspective).
Other info from Epicurious.
I do not have experience with mud cake. If it isn't a very sturdy cake, you may need to add supports (i.e. dowels and cake rounds). If it is sturdy like a yellow or white cake, you can stack them without adding supports.