When a voltage gradient across a dielectric becomes too large, the material will break down and become conductive, mostly because of plasma ionization. Thus we get lighning, static electricity fingertip shocks, and tesla coil shows. But often during such breakdowns, there are multiple, simultaneous, breakdown paths. Why? Once one path is created, isn't that now-conductive path far superior for current to flow through? That is what causes the arc itself to extend almost instantly since the now-conductive partial arc is even closer to the opposite electrode/ground and thus the same potential difference has a shorter seperation, creating higher field which causes even more runaway arcing until the spark joins the two. But once such a conductive path exists, why would another one occur simultaneously? For example, a bolt of forked lightning? After thought, I imagine it would be because one or both of the opposing potentials is resistive and can't handle the current and thus it accumulates charge (like a capacitor) until the resistive earth near the stroke is effectively at a high potential, until an alternative path to a different patch of earth is also a candidate. In the limit this would happen multiple times, and recursively, giving path branches like this. But this doesn't explain why you'd get lighning branches that terminate inside the nonconducting dielectric itself. Why does lightning fork into tendrils that do not reach the ground? Surely the air cannot accumulate charge locally! Unless it's accumulating on raindrops? But that's not true, you see this with Tesla coils in dry air as well. Where is the current going? Surely there's not one air molecule at the end of each tendril accumulating coulombs of charge! And also unexplained is how there would be multiple paths between highly conductive materials like metal electrodes. Here it's really clear that there's no local resistance to allow any local charge accumulation. Why are there multiple small arc paths instead of one big path? My thought that would help explain this itself is that the air (or dielectric in the plexiglass example) itself has limited current carrying capability, especially after it's heated so much that it has expanded into lower density. But then why wouldn't the breakdown just keep enlarging the plasma tube (which is easy) instead of breaking down in a brand new path? I suspect the answers involve plasma dynamics and the effect of spatial charge in the arc itself pushing the arcs apart, but I can't get even a qualitative feeling why that would create multiple paths between conductive electrodes.