How does current flow in a irregularly shaped heterogeneous resistor? The motivation for my question is understanding how electricity gets through your skin as opposed to running along it, and how the presence of things like water on the skin affect the relative deadliness of electricity, or ability of it to permeate the skin. 
I don't understand how to view the body as a resistor, as the skin, and all the components of the body have different resistances and thicknesses. How do I know what parts of the body carry significant current? And how much current in total?
 A: There have been attempts to model the body and study what happens during discharges, like from a taser.  Finite Element Models (FEM) for testing human body are pretty accurate.  Here's an example of current density distribution due to a shock to the skin and how the current flows.

Where the physician's report described the body's response to current flow:

Current decreases rapidly with distance from electrode. The fat and
  skeletal muscle layers have an electric shell effect on currents that
  reach into deeper tissue layers (such as the heart): -The fat layer
  attenuates the electric field by at least 25 times, even under
  worst-case minimal thickness assumptions -Skeletal muscle preferred
  longitudinal (with the grain) electrical conduction diverts about 88%
  of the current away from deeper tissue layers
In the muscle layer: -the transverse current density is less than 15
  mA/cm -the equivalent field strength is in the 15-30 V/cm range:
  greater than 2.25 V/cm – threshold to capture motor neurons but much
  low lower than levels required for irreversible electroporation (1600
  V/cm – Gehl et al. 1999
The fat and skeletal muscle layers significantly reduces the current
  that reaches deeper into the body. The skin-heart minimal distance for
  typical in-custody suspects is at least two times greater than the
  maximum distance estimated by theoretical models as being necessary to
  induce VF [ventricular fibrillation]

A: Firstly, let us construct a proper model for your purpose. The skin has a very high resistance(on the order of hundreds of kilo ohms) when it is dry. However, when the skin is wet, salt on your skin is dissolved and along with water, fills the pores in your skin, creating a highly conductive path (on the order of hundreds of ohms, thanks to conductivity due to ions present in the water) through the skin. But beneath your skin, there are all sorts of conductive materials filled with ions, especially your blood.
Now, the way body works as a conductor will vary depending on how it is being shocked. If we are inspecting a microshock, for example if a catheter inserted into the heart is not grounded properly and is at a nonzero voltage, then, if the patient touches the chassis of a grounded electronic device, the path of conduction will be:
Catheter - Blood - Heart - Rest of internal structure(mostly blood) - Skin - Chassis
Now in this case, most of the resistance comes from the skin interface (Order of 10 - 100 ohms from inside the body vs. Order of 100 kohm's from the skin). However, In the case of a microshock, a few micro amperes are enough to cause the heart to enter into a state of fibrillation, killing the patient in a matter of seconds, since all of the current flows through heart.
However, if the shock is a macroshock, both sources are located outside of the body. In this case, the current will have to penetrate the skin twice, in a manner as follows:
Source 1 - Skin - Blood & Tissues - Skin - Source 2
Again, the skin causes most of the resistance, and this time there are 2 skin interfaces, causing half as large current as a microshock. However, the major difference now is that the current is distributed throughout the entire body instead of being focused on a crucial organ, therefore an order of hundred milliamps may be necessary to cause any life threatening damage.
Summary:


*

*You may treat the skin as the only source of resistance in most cases(if the skin is dry).

*The life threatening aspect of electricity is more related to how the shock is applied as opposed to the magnitude of the current. There are lightning strike survivors, yet people die to microshocks every now and then.
