Contacting prospective advisors before graduate school applications - courtesy or annoyance? Last year, rather late during the MSc application cycle (after one round of funding was allocated - tardiness due to an abrupt change in my life situation), I emailed two professors from two schools that I most wanted to go to. I had perused their webpages and decided these professors had the specific research interests closest to my own.

My reason for contacting them before finishing my applications for their respective schools was that the applications included a large section for specific research questions that I wanted to investigate. So, I emailed these professors asking a bit about their work, because their webpages of course featured surface-level stuff.

One professor was very receptive and invited me to Skype with her so she could better explain herself and I could ask her questions. With her support, I was able to write an application that met her standards quite quickly.

The other professor told me - paraphrasing, of course - that he was too far into the process of choosing a new student for his research group to spend time helping me finish the application.

Let me be clear that the latter professor didn't say any harsh words and I have nothing bad to say about him. That said, the purpose of my question is to decide whether it's better for me as a prospective MSc student to email professors ahead of time like this. Was the latter's rejection likely due to my tardiness rather my emailing him? The more receptive professor made the point that she always wanted to have prospective MSc students write their own research proposals and get her approval before submitting the application. Is this common? If so, then I guess reaching out beforehand is a good thing to do, but earlier in the application cycle?

Thank you.
Actually, it can be either a courtesy or an annoyance, depending on a number of things. A cold email from a student in an unrelated field that looks like a mass mailing is clearly annoying and will be discarded without an answer. But an initial contact from one of your professors with a recommendation to look at you, especially if they are colleagues, will meet with success. Most contacts are somewhere between these extremes. 

I think you were lucky to get responses from both. The fact that neither was dismissive suggests you had a good approach. 

The prof who refused you, I suggest, was being honest. Others were in the pipeline already and there was little time, as you say, to make a good and fair analysis. 

I don't recommend sending out resumes blindly to a bunch of folks. It is unlikely to result in any success. But when you are stuck and in a time bind yourself, you do what you must. But having a faculty advocate initiate a conversation in your case might have been an even better way to proceed. 

And, as always, do your homework. If your background and interest are aligned with those of the recipient you stand a better chance. Even better if you can indicate that you know something about their work. Blind praise of their work, not knowing what it really is, is easy to detect and such letter easily slide into the trash.