Dovahkiin of your choice is fighting Alduin in Sovngarde, and just as he/she lays a killing blow they're transported to Middle Earth because ~*magic*~.
Of course Thorin & co stumble upon the dragonborn at some point of their journey

Could be gen or any pairing of your choice, just no incest please

+A bazillion points is the dragonborn is an Orc

http://hobbit-kink.livejournal.com/9471.html?thread=20433663#t20433663