There have been several contenders already- The Pullman trilogy, the Lemony Snickett series, the Artemis Fowle books. They've all been successful, but none of them has come near repeating the Potter effect.
International, cross-cultural, intergenerational, cultic- causing obsession, causing 36 hour queues for product, making the headlines.
Marketing has a role to play, but you've got to have a decent product first- a product that a significant number of people have fallen in love with.
Rowling came from nowhere- an untried author who was rejected several times before getting a deal with a small-time publishing house. Her success is implausible, a-million-to-one.
Why Harry? Why not? These enthusiams sweep the world from time to time. You can trace them back through history. It's not just about books. People fall in love with all sorts of cultural products. The last really big one was Star Wars. And before that there was Beatlemania and before that James Bond and Sherlock Holmes and the serial novels of Charles Dickens. People thronged the quayside in New York as the boat came in carrying the latest issue of Old Curiosity Shop and shouted up at the passengers, "Is little Nell dead?" No concern about spoilers there.
You can't go any further back because the phenomenon depends on modern communications.
It's a feature of all these fandoms or whatever you want to call them that the product is doled out in installments, with the public always expecting and wanting more- another album, a further episode, the next movie. The relationship builds from year to year. The fan lives alongside her heroes in real time. And it's a reciprocal relationship- with give and take between creator and audience. The "author" becomes a celebrity- gives interviews, bats away speculation- Conan Doyle brings Sherlock Holmes back from the dead because of pressure from his readers. And it gets to be quite erotic too. The Beatles have to hide their real marriages so as not to upset the fans, girls queuing outside Waterstones say (only half joking) that they want to marry Harry Potter.
(And then there's fanfic. And slash.)
Another common element is that all the biggest fandoms centre on work that's really quite good. We still read Dickens, we still listen to the Beatles, the James Bond franchise is still lumbering on. The public en masse turns out to have pretty good taste. I can't think of an instance where the idolised work was total dreck. Star Wars? Well, The later movies were dreadful, but the first ones weren't.
And one of the indices of their quality is that all these fandoms gave us something new. None of them repeated the success of an earlier franchise. They weren't carbon copies. Which is why all those publishers who are looking for something as much like Harry Potter as possible are barking up the wrong tree.
The next big thing could be anything. And it will take us by surprise.