What is the core of the lightning?
I found the paper you initially referred to here:

http://onlinelibrary.wiley.com/doi/10.1029/JB073i006p01889/full

based on the hyperlink by the xkcd webpage you referred

http://www.agu.org/pubs/crossref/1968/JB073i006p01889.shtml

The full reference for this paper is: Oetzel, G. N. (1968), Computation of the diameter of a lightning return stroke, J. Geophys. Res., 73(6), 1889–1896, doi:10.1029/JB073i006p01889.

In the abstract:


  The diameter of a first return stroke is found to lie in the range 1–4 cm. Subsequent return strokes are smaller, with diameters in the range 0.2–0.5 cm. In many cases, strokes to towers have shown evidence of the smaller strokes occurring alone. These are explained as strokes initiated by an upward leader.


This paper is quite old - but is relevant nevertheless.

A more recent paper review the physics of lightning in this review paper, titled 'The Physics of lightning' by Dwyer and Uman (2014). They present the various steps implied when a lightning form, illustrated by this illustration (Figure 1):



Basically, there is several stages when a lightning strike. There is the stepped leader component, that somewhat lead the way for the exchanges that will follow. In the figure, we notice the positive and negative signs (+ / -) and how they change position depending on the discharge.

The stepped leader can be followed by return strikes and so on. In this paper they mention diameters for the stepped leader, which may appear to be much larger than the return stroke, such as in the range of one to ten meter in diameter:


  The luminous diameter of the stepped leader has been measured photographically to be between 1 and 10 m. 


But - this is by using photography - yet the core of the lightning at the center (the core) seem to be a few centimeter in diameter:


  It is thought, however, that most of the stepped-leader current flows down a narrow conducting core a few centimeters in diameter at the center of the observed leader. 


So in the end both papers tend toward similar centimeter-scale measurements for the lightning core.



The core: aforementioned literature refer to the component of the actual lightning as a 'current carrying core' surrounded by a corona sheath. The sheath is what appear to be 1 to 10 m in diameter, where the actual 'electricity channel' is centimeter wide; 

so this core as the centimeter wide channel is the electron pathway.