Why does lightning generate multiple branches?

I know this is a little more than you asked for, but lightning is very interesting.

A lightning event is usually called a flash and lasts about 0.5 seconds. It consists of a near-invisible stepped leader followed by a very bright return stroke backwards along the path of the stepped leader. Following the first stroke, there may be additional strokes in the flash, following nearly the same path of the first one. There may be slight deviations due to other dim leaders called darts.

Over half of all lightning flashes happen within a cloud and are called IC discharges. The type of flash of most practical importance is the cloud-to-ground (CG) lightning. Other rarer types of lightning are cloud-to-cloud and cloud-to-air flashes. Note that the bright flash that we see is the return stroke, so cloud-to-ground lightning will appear to start near the ground and zoom upward; the initial stepped leader happened first, starting in the cloud.

The typical charge separation in a cumulonimbus cloud results in the top of the cloud having a net positive charge, near the bottom having a net negative charge, and occasionally the extreme bottom edge having a small positive charge. The overall effect is that a large negative charge (of magnitude 15 coulombs) is closer to the ground than the positive charge. This charge structure causes the ground to become positively polarized as negative electrons are ``pushed'' away by the cloud.

Air is normally an insulator, but if the charge separation per distance is too large (either because of large charge or small distance), it can become a conductor. The initiation event is unknown, but scientists currently speculate that either atmospheric radioactivity (from Radon-222) or creation of ions from stratospheric reactions with cosmic rays (solar protons, other charged particles, or high energy photons) can trigger a flash.

In any event, negative charge moves in steps about 50 meters long through a small conductive pathway in the air, pausing from 20 to 50 microseconds at each step, reaching the ground in a few hundredths of a second. The current in this leaders is between 100 and 1000 amperes. After each step, the leader shifts direction as a new conducting path opens.

After the leader reaches the ground, a tremendous burst of energy is released in the return stroke along the path of the leader as the positive ions in the ground and electrons in the leader combine. This recombination produces a current of 20000 to 30000 amperes, and a temperature as high as 30000 K. The temperature of the surface of the Sun is 5800 K. This tremendous release is accompanied by a bright optical flash, an electromagnetic pulse, and the rapid expansion of heated air. The typical size of the return stroke channel is 1-2 inches in diameter.

If the initial stroke doesn't resolve the charge separation, more charge from the cloud will travel to the ground along the original path. This is called a dart leader. When it reaches the ground (about 10 times faster than the stepped leader), an additional return stroke occurs along the path. The time between strokes is on the order of hundredths of seconds but could be as long as a tenth of a second. Anyone watching a lightning storm has seen multiple strokes along the same pathway.

Lightning branches so that it can reduce the resistance of the path it takes to the ground. As you know, when you attach two identical resistors in parallel, the equivalent resistance is lesser than that of the two in series. Branching essentially does that. It creates more and more parallel paths by which the electrons can flow, thereby reducing the total resistance of the journey from sky to ground.

The mechanism of how it branches is similar to that of rivers branching. The water streams branch when they approach a solid mass so that they can move with lesser obstruction around the mass.