UKH

You've fallen off a traverse or out into space over an overhang. What is your weapon of choice for climbing back up the rope?

Whatever I have with me.

I always have prussic cords on my harness, so would be those. But if I'm seconding when this happens and I'm being belayed with a guide plate (Pivot or similar) it's likely going to be more efficient for the belayer to do a quick haul.

As already mentioned, whatever I've got. Although that normally involves the choice of a couple of prusiks, a Tibloc and a Micro Traxion.

If it's only a short distance I'd probably just go for a couple of prusiks. Tiblocs are slightly more efficient but prusiks never run the risk of rope damage. Also I might just use a 120cm sling rigged as a Kleimheist as the foot loop. 

If longer, then exactly the same initially but once I have some slack I'd be very tempted get my Micro Traxion clipped to my harness and rigged for progress capture.

However, when I did have to do this recently on some crazy steep E4 at St Govans I wasn't exactly efficient and it resulted in a ludicrous amount of swearing. I also can't remember exactly what I did other than more practice of this stuff is always required!

I'm dubious about this? I'd agree that an assisted hoist is faster, but hauling your mate up using an unassisted hoist is pretty flipping nails and hauling them up more than a metre or so would be far less efficient than just the second prusikking up the rope. 
 

Like longsufferingropeholder said, whatever I have with me, it is perfectly possible with a couple of slings or even shoe laces... although that doesn't mean you will enjoy doing it.

I've got a couple of 'get out of jail free' crabs I like to have on the back of my harness that make dealing with things like that a whole load easier, and for the total weight of 230g including the biners it doesn't feel too heavy to carry for the just in case moment.  They've come out a couple of times, usually for getting out of a wet sea cliff though! 

Added the photos for interest; Nano traxion, Tibloc, Beal Jammy, trango piranha knife and 2x smallish crabs. Great for hauling gear and people, ascending ropes, cutting cheese, top tope soloing etc.

My shoelaces, obviously: youtube.com/watch?v=8FDX6_BSas8&

More sensible answer - although I did used to climb with someone who was rumoured to use prussic cord for his shoes laces, just in case!

Have always got a prussic on the back of my harness and on long/sea cliff/whatever routes I'll carry 1 or 2 Ropeman mk2 (that I picked up in a bargain bin somewhere) if I think they might come in handy.

They were certainly useful when I ab'd into Subluminal Cliff once and it started snowing while my partner was 1/2 way down!

I use two Ropemen and some 6mm tat already rigged for Single Rope Technique ascent.  Sits in a wee bag on my harness.  A zillion times better than farting about with prussic loops, random slings or boot laces.

I've used this to derig a few cave pitches but you do have to be careful not to drop one of the Ropemen when attaching it to the rope!  Its worth securing them with some 2mm tat.

I tried a Tibloc....  (shudders at the memory...)