Here's a video taken at a recent Angelus address, where the Holy Father is releasing a couple of doves from his window. As you can see, the birds aren't too eager to fly away, and one of them circles for a moment, and dives into the window, flying over the pope's head. Pope Benedict, always unflappable, says, "Mama mia! They want to be in the Pope's house!"
Apparently there are a lot of Anglicans who feel the same way.