There's a fair amount of research to answer the question of whether two monitors are better than one for varying types of work, and the answer is generally "yes". The article "Are Two Monitors Better Than One?" is a good starting point if you're interested in that research.
However, your question is specifically about how to layout windows in the same application when using multiple monitors. To my knowledge, there isn't any public research on that. In my own experience (I've worked on IDEs, word processors, presentation software, mail applications, and virtual infrastructure software), users tend to want what they are focusing on showing on the screen that is directly in front of them, with helper windows/applications/documents/whatever on the secondary or tertiary monitor. (I personally have a three-monitor setup in my office: my laptop screen and a matched pair of 24" displays.)
Based on my experience, I think that your application should be flexible enough to allow your user to move your application's windows around to where they want them to be. It's important to remember that your users are unlikely to always be in a situation where they're using a multi-monitor setup -- laptops are now more common than desktops, and they're mobile for a reason. Your application should continue to be useful if I'm on my 13" laptop as it is when I've got my 13" laptop hooked up to one or two external displays.