I recently hit 80 on an alt and farmed random heroics for a while, and here's my statistics:

3 Ingvar the Plunderer kills (Heroic Utgarde Keep)
3 Keristrasza kills (Heroic Nexus)
3 Anub'arak kills (Heroic Azjol-Nerub)
3 Herald Volazj kills (Heroic Ahn'kahet)
3 The Prophet Tharon'ja kills (Heroic Drak'Tharon Keep)
3 Gal'darah kills (Heroic Gundrak)
2 Sjonnir the Ironshaper kills (Heroic Halls of Stone)
2 Loken kills (Heroic Halls of Lightning)
2 King Ymiron kills (Heroic Utgarde Pinnacle)
2 Cyanigosa kills (Heroic Violet Hold)
1 Ley-Guardian Eregos kills (Heroic Oculus)
1 Mal'Ganis defeated (Heroic CoT: Stratholme)
0 The Black Knight kills (Heroic Trial of the Champion)
0 Devourer of Souls kills (Heroic Forge of Souls)
0 Scourgelord Tyrannus kills (Heroic Pit of Saron)
0 Lich King escapes (Heroic Halls of Reflection)

The order I got the heroics in is:
1. Ahn'kahet: The Old Kingdom
2. Gundrak
3. Drak'Tharon Keep
4. Utgarde Keep
5. Utgarde Pinnacle
6. Halls of Lightning
7. The Culling of Stratholme
8. Azjol-Nerub
9. Halls of Stone
10. The Violet Hold
11. The Nexus
12. The Oculus


All heroics were done as random, none were queued for directly.
All were queued solo as dps.
All groups were successful clears, and I never left any groups early.
I still haven't gotten ToC or the ICC 5mans (even though I'm able to select ToC and FoS in the dungeon finder, so my gear is high enough.)