How much should your POI's research interests match yours?

[Notker the Stammerer]

I'm looking at PhD programs for Fall 2013. My primary interest is the interplay of politics and religion in Early Modern Britain. Should I try to find a professor with exactly those interests? What about a professor who specializes in Early Modern European religion and politics, but not specifically Britain? What about someone who researches Early Modern Britain, but not religion in particular? I'm not finding many professors with exactly my interests, or at least as far as I can glean from the sometimes sparse information on college websites.

[Simple Twist of Fate]

I'm going to do something dangerous and try to make a generalization. It has seemed to me that profs at the top programs can afford to be more choosy, because they often have dozens of well-qualified potential students to choose from. The result is that if you apply to work with a well-known professor at a big program, the chances are that your qualifications (GPA, GRE, LoRs, writing sample) are probably matched by a number of other students. What sets you apart is the novelty and fit of your research interests. In the middle-tier programs, profs might also have dozens of students, but they may be more willing to consider other factors to compensate for an imperfect fit.

I also had a set of interests that not many professors tend to specialize in. That's one of the things that I find so exciting about my interests - that they're relatively "virgin soil" so to speak. My experience is that some professors are more willing than others to take on students with somewhat diverging interests - roughly according to their "prestige".

The best advice I can give is make a running list of profs. with interests that are in some way related to yours (by looking through the work that most interests you, by cruising the faculty profiles of various schools, and by asking your professors if they know anyone with your interests) and ask them over email if they would be interested in a student with your research interests (keeping in mind that a no-response doesn't mean they won't consider your application, and a friendly or even enthusiastic response doesn't mean they'll support your application).

Good luck.