How to request source code?

Whether common or not, it is acceptable to ask. Ask the main professor, who may pass on the request to a co-author.

I'd suggest that you only give a small amount of detail in the initial request but offer to say more if you like. But don't flood the professor in the initial request. Mention that you have a draft, but don't send it. And you can certainly mention that you are interested in applying to the university.

What happens next depends on the nature of the reply. Perhaps they will want to help you, but other outcomes are possible.

Is it common to just email and ask for the source code or would that be considered somehow inappropriate?

It's not improper to ask. Consider some core values of the scientific world:

• Reproducibility: for research to be truly valid, others should be able to reproduce it. This is why publishing source code is encouraged.

• Standing on the shoulders of giants: science is all about building on each others' achievements. My discovery may help you and your discovery may help me. It's not a zero-sum game.

Who is the appropriate person to contact? All of the papers on the model have been published by by the professor and the same two co-authors, some with additional co-authors. Should I email the professor himself, one of the co-authors, or all of them?

Now, what is the best way to ask? You can email directly, but it would be nice if you can find a mutual acquaintance that can introduce you.

Is there anyone in your department (maybe your supervisor) that has met this professor before? One of the reasons scientists go to conferences is to build these networks. Or maybe someone in your department has co-authored something with the professor or his co-authors; go through the professor's publication list and look for familiar names.

Ask your supervisor if they know anything about the professor that's relevant. It's part of the supervisor's role to know the field and use it to advise you.

In the end, who you contact is a bit opportunistic. If you have a good connection to one particular person, start there.

How much detail about my own research should I include in my email? Just what's sufficient to justify the request or more, possibly a draft of the proposal?

I would keep it reasonably short. Enough to justify the request, certainly. But in general you don't share draft proposals until you've gained whatever grant you're applying for.