Once you’ve beaten Alduin’s full share of mortality into him, he begins writhing and thrashing on the ground- then gradually explodes into black sludge which dissipates with a loud crash.  Nothing remains of him, not even a soul for you to use.  Tsun congratulates you on finally slaying the mighty dragon, and the three who helped you cheer you on as well.

You can speak to the three of them and hear a few praises and stories, but there’s really not much else to do here.  When you’re ready to go, speak to Tsun- he will teach you a new shout to call a hero from Sovngarde to aid you.  Then he will Shout at you- and drive you from Sovngarde.  Curiously, you return not to where you left the ground, nor to Skuldafn- instead, you land on the Throat of the World, near Paarthurnax’s wall.  You also return surrounded by dragons.

The dragons take turns Shouting together about the death of Alduin and flying off from the mountain, so don’t worry about having a brawl up here in the limited space.

If Paarthurnax is still alive, then he is second to last to launch- he will explain to you that while he is not necessarily upset, he isn’t glad that Alduin is dead either- the Devourer was once his comrade, after all, and was the oldest of all Dovah.  The ancient white dragon goes on to explain that the world will continue and any next world is on its own.  For himself, he intends to seek out other dragons and shout them the Way of the Voice in the hopes that they will listen and follow him.  He then flies off to the North, but will return to his usual perch as soon as the last dragon is done speaking with you.

Last to leave is invariably Odahviing, who lands on the ground beside you to talk.  If Paarthurnax still lives, Odahviing is scornfully amused at the idea that the dragons will follow the white’s ‘ridiculous’ Way of the Voice, and insists that while he’s perfectly happy to be free of Alduin, he sees no merit in Paarthurnax himself.  Either way, Odahviing claims that you have proven yourself twice over and, as your Thu’um is clearly the greatest, he will heed your call, should you ever give it.  This means that from here on out, you can use the Od Ah Viing shout to call on him to aid you in exactly the fashion most dragons seem to prefer to attack you.  Odahviing then takes off, and circles the Throat of the World for a little while before flying off.

You may talk to Arngeir if you like- while he is uncertain if Alduin will ever return, he admits that whether or not this happens is up to the gods to decide.  Delphine, on the other hand, is quite glad to hear the news- not that this will change her mind on the Paarthurnax issue, assuming you haven’t killed the white.

With the main goal of saving the world of Tamriel now complete, you’re free to gad about Skyrim and poke your nose and fingers into other peoples’ business all you like.  Congratulations!