Your example sounds promising! I haven't apply to the PhD programmes yet, but I approached professors at three universities over email, we discussed my background, interests and research topic, I sent them a draft of my research proposal. Eventually all three of them told me to apply and be sure to indicate their names on the application form. As for details of my research,we will discuss it when I start (exact words of one of them). Does it sound as an unofficial offer, I wonder? What are your thoughts?