If you have content and time to really maintain those three sites properly, then do it, each one will get their own set of visitors and that will generate reputation, traffic, links, etc. Since each one will have it's own life, the interaction between them will be good.
But, if those sites are poorly maintained, then the only real relation is going to be between themselves and that is not good. First, why dump garbage on Internet? second, Search engines may recognize the trick/scam/situation and penalize it. Third you are going to be wasting time and money for no good reason.
So it boils down to the fact that if you have quality content, then one specialized site per subject is a good idea. Of course I'm assuming each one will have different content, not slight variations of the same subject.