Friction in absence of normal reaction (in the context of macroscopic picture) Take two flat non-smooth ($\mu\neq 0$) surfaces and rub them against each other. You feel the friction as you are doing work to displace them relative to each other.
We usually think that friction originates due to relative motion of contacting surfaces. But I think we miss this important point that even before relative motion we must check for existence of some mutual normal reaction.(This however has nothing to do with the fact that$ f<=\mu N$ which is just an upper limit and so one might mistakenly take the appearance of N in the equation to mean some direct correlation).
So the question is can frictional force act in absence of normal reaction, given that relative motion is there(eg. sliding of surfaces against each other in gravity free space)?
 A: Friction is an adhesive process. The friction isn't caused by the load, what the load does is flatten asperities on the surfaces and increase the area where adhesion can take place. For a discussion of this see How is frictional force dependent on normal reaction?.
So you can have friction without a normal load if the surfaces are already smooth enough for large areas of contact to exist. An example of this is cold welding.
A: Are you suggesting that friction could come about as a result of the Normal Force (Fn) between the two interacting objects?  
If so, Normal Forces act only perpendicular to an object's surface (opposite to the force of Gravity. The Normal Force serves basically to prevent solid objects from moving thorough each other.  
Friction implies some horizontal motion (parallel to the surface), thus if a force is applied between the two pieces of paper in your question, there would be a component perpendicular to the surface, Fn, and one parallel, Ff, which is friction.  
A: Macroscopic friction forces depend on two types of microscopic physics.

*

*Long range forces between interfaces.
Two surfaces which are not in physical contact exert on each other long range
forces. These forces are due to the interaction of the molecules in the last layers, close to the surface of the material. They can be hydrogen bonds, Van der Wall's forces or Pauli exclusion in nature. One can read in this paper  that friction coefficient changes by two orders of magnitude depending on the absence or presence of hydrogen molecules on the surface. Vertical intermolecular forces sum up to macroscopic adhesion force, while lateral ones sum up to friction forces.


*Coulomb's friction force is different in nature. The Coulomb's friction force is the force necessary to tear material away. It is proportional to $S_{contact}$, the physical area of contact between the two surfaces which is a lot smaller than the macroscopic surface.
$$ F_{Coulomb} = \tau _{c}~S_{contact}$$
where $\tau _{c}$ is the yield stress during shear. One can prove that:
$$ S_{contact}= \frac{F_{N}}{ \sigma _{c}} $$
$ \sigma _{c}$ is the penetration hardness, i.e. the largest stress the material can bear before plastic yielding.
Combining these two relations we get:
$$F_{Coulomb} = \frac{ \tau _{c}}{ \sigma _{c}}~ F_{N}$$
In plain English:
The more you push down, the larger $F_{N} \nearrow$.
The larger $F_{N}$, the larger the surface of contact ($S_{contact} \nearrow $).
The larger $S_{contact}$ , the more material to tear off.
The more material to tear off, the larger the force $F_{Coulomb}$.
The Coulomb's friction force is the maximum force to apply before tearing appears.
The model is very crude but catches most of the physics. Long range forces and Coulomb's force are always both present, the former dominate the static case, the latter the kinetic one. Their relative importance varies with the conditions, that is why it is not uncommon to have large departures from the Coulomb's force.
Tribology is the branch of science dedicated to the study of friction force. You can get a good idea of the field with these two books:
Contact Mechanics and Friction Physical Principles and Applications -Valentin L. Popov.
Sliding Friction Physical Principles and Applications
