Would you die if you put your hands on a powerline? You know how birds perch on powerlines without getting electrocuted? What if by some chance that I find myself falling and I grab on one of them? Let's say both of my hands are on the same line, would i get electrocuted?
I am thinking I won't because the current won't rush through me and I won't be part of the circuit - me - powerline. 
How does the ground play a role in this? I've heard people say that the ground creates a potential difference, but how? There is only voltage across the powerlines, the pole connecting to the ground is wood, an insulator?
Thanks
 A: Hanging from a power line you should be as safe as a bird.
The voltage difference is between the lines (e.g. in a 3-phase system) and between the line and ground. This voltage difference exists across the insulators and pole, as well as through the air to ground. These voltage differences are obviously small enough to avoid striking an arc, hence no current flows between the lines or between line and ground. If you are hanging from one line, there is no change in the separation between the lines (unless you are swinging wildly) and hence again no current flows between the lines. As the distance between the lines will usually be smaller than that between your feet and the ground, again no current will flow, and you will be safe. Note that, if this distance were too small, you would not be safe standing under the line either! 
Your real problem will be to get down from the line. Unless someone can switch off the power, or you are an acrobat who can jump from the lines to the pole, you will need to touch both the line and the pole simultaneously. If you are hanging from high voltage lines (tens of thousands, not hundreds), touching even a wood pole at the same time as the power line may kill you, unless the wood is extremely dry. Even though wood is considered a poor conductor, when it gets damp its conductivity increases dramatically.
A: Have you seen the helicopter crews that work on overhead lines approach a live wire. They extend a conducting pole and equalize their voltage with the line. After than it is "safe" to work on the line. As long as there is a conductor connecting them to the wire it is ok. Of course the initial equalization process would kill you if the arc went through your heart instead of the conducting pole. 
YouTube video of what I am talking about is seen here.
So in theory, yes it would be safe, if conditions are ideal, and everything else stays way away from you, so you don't arc to a nearby tree or something.
PS. It is never "safe", just "safer".
A: There actually is a current that moves through your body, albeit it not enough to hurt you. You don't need to actually touch the powerline, just standing near it will cause a current to flow in your body. If we model a single powercable hanging a height H above the ground as an electric charged cable of infinite length hanging a height $H$ above a perfect conductor, then the electric potential relative to the ground a distance R below the cable is:
$$V(R) = V_0 \frac{\log\left(\frac{2 H}{R}-1\right)}{\log\left(\frac{2 H}{R_{0}}-1\right)}$$
where $R_0$ is the radius if the cable and $V_0$ is the voltage relative to the ground. E.g. if you take $R_0 = 10$ cm , $V_0 = 10^6$ Volt then the optential difference between the head and the feet of someone 1.8 meters tall a meter below the powerline will be approximately 166,000 Volt. Now, this voltage has a frequency of 50 Hz and the human body has a finite resistance and electric capacity, so currents will flow in the body in response to the electric field. But these currents are not very strong. Even if the body had zero resistance so its potential were constant, then that would only require a small amount of charge to be moved around to neutralize the 166,000 Volt.
