This seems to be a trick question. Are there universities which will "give you a PhD" in a short time? Well, yes. If you work hard enough to "earn a PhD" in a short time.
That said, it is quite common in continental Europe for PhD positions to be offered for a period of 3 years. That's nice if your Masters degree has already prepared you with the relevant graduate-level concepts. You will still have to find a PhD topic and complete your investigations in the stipulated time.
On the down side, PhD supervisors (who may even be a Postdoc or a researcher with individual grant) usually find it difficult to arrange for additional funding if you are unable to produce satisfactory results within 3 years. At good universities, and in well-funded disciplines, this is usually not a problem. But this really happens, and if you do not come from a first-world country, it may get difficult to sustain yourself.
Publication limit? It again depends upon your field. In theoretical fields, like pure mathematics, theoretical physics, some branches of computer science, etc. it is difficult to publish, so you may get a PhD with one or two papers. But in experimental fields, it is difficult to put a number. That shouldn't bother you though, because your supervisor is usually there to help you out.
And PhD is after all a training in becoming an individual researcher. So why bother about number of publications already? What you should worry about is, do you really want a PhD? There, your query suggests only a superficial motivation.