Where does a string tighten when you pull it? I have the following setup:

The string of negligible mass, causing little friction, is shown in dark blue and is fixed at the red circle. The taut string is shown in light blue (with excess string removed). I have shown an orange arrow which indicates the direction in which the string is being pulled. Importantly the force is always exerted at that location and any excess string is removed.
I would like to know how the string deforms over time as it is pulled from that point (orange). Does the end closest to the pulling force move first and straighten up, wrapping around the object 'A' early on, or does the whole string change shape continuously?
How does the direction of pulling force affect things if at all?
Thanks in advance.
 A: While it is slack it will depend on the type of string and the transmission of forces. There will be an impulse propagating across the string starting from the left , there might be rotational energy while it is slack. Think of the molecules composing the string, they transmit the force to their neighbor.
Once it tightens it will depend on the actual geometry. In your drawing it will meet A before all the slack is taken so some frictional force will enter. 
A: 
I would like to know how the string deforms over time as it is pulled from that point (orange). Does the end closest to the pulling force move first and straighten up, wrapping around the object 'A' early on, or does the whole string change shape continuously?

For a better understanding,
Take a look at this figure( I've modified the diagram in order to explain things in a better way )

When the string is pulled, the coil of wire( initially slack ) as shown in region $B$ begins to uncoil. What you will observe is that the portion of the wire in region $A$ begins to  move only after the coil of wire in region $B$ gets completely uncoiled( it remains slack until then ). Try it out with a thread or a chain. This is to show you that the portion of the wire close to the pulling force will move first followed by the other portions of the wire.
