What is the origin of spin of celestial objects? In an older question from June 2011, Why does each celestial object spin on its own axis?, apparently revived by the system, a user is
asking about the origin of the rotation of celestial bodies.
The accepted answer (with 17 votes) states the following:

When things collapse under their own gravity in space (i.e. clouds of gas and dust), any small amount of asymmetry in the collapse will be enough start it spinning.

And then it goes on saying:

Even if it spins by a tiny amount, as it collapses, angular momentum
    conservation will mean it spins more and more quickly.

Is all this really correct?
I could try to ask in a comment to the answer. I actually did. But the
author is no longer registered.
Hence I am asking it as a question.
But that is not the end of the story. As I was about to ask my
question, I looked for other relevant questions, and there are some. I
did not make an exaustive survey, but I did not find one that had
satisfactory answers:


*

*On the origin of the rotation of celestial bodies
(december 2011)
has just one accepted answer (0 votes) stating essentially that the
solar system has angular momentum because it started from a cloud
that had angular momentum. No comment.

*Why does everything spin?
(july 2011) is questionning about everything from galaxies to electrons. The
answers are of a much higher quality, but while they seem to justify
the possiblility of spin and angular momentum (and its conservation), there are not clear on how it appears, at
least for celestial bodies.

*Origin of motion and relative speed of bodies in the universe
(june 2013): That
was my own very naive first question on this site. It is related
but does not directly address spin.
One answer I found is that momentum appear from bodies in relative
motion past each other. Nice, but not really an answer: where did they get their relative speed to begin with. Unfortunately the answer is: from the angular momentum of larger structures they belong to (well, it can be more comples). So this is just chicken and egg explanation. But how did it get started?
Note that my question is not a duplicate, since it is primarily
whether the above statements are correct, which is not considered in
these other questions.
Furthermore, these questions are fairly old, and given that none had
received answers that seem to answer the question of the origine of
existence of celestial angular momentum (not in a way I can understand
anyway), it may be appropriate to attempt restarting the process, with
the above discussion to motivate that an answer should explain the
physical mechanism that started the existence of spin of celestial
bodies.
 A: I asked the question because I did not believe in the accepted answer
that has been sitting for more than 3 years.
I have my own understanding, but since it is not good practice to put it with
the question, I am posting it as one possible answer.
My problem is that I do not believe the first statement quoted in the
question which is
contradicted by the second quoted statement. If there is such a thing as
angular momentum conservation, I do not see why assymetry alone should
produce angular momentum on the assymetric structure.
If the cloud is isolated, it should collapse - period. The assymetry
may possibly create some internal spinning (adding to zero angular
momentum), but certainly not any global spinning, no global angular
momentum, as clearly stated in this first statement.
What can induce spinning in the collapsing cloud is (gravitational) interaction with other external structures. And it is a fact that such external structures always exist.
That may be obvious for the author of the answer, or professional astrophysicists, but it is certainly not obvious for laypeople. Hence I do consider this answer misleading at best.
Furthermore, if such external interacting structures exists as they must, then the asymmetry hypothesis is no longer needed, as it will be created by these interactions.
Angular momentum can be "created" only
by exchanging angular momentum with another body, so that each gets
one of two opposite angular momenta, that sum to no momentum. Then
each can go its own way. Of couse, there is globally no creation of angular momentum.
I am not quite sure about the dynamics of the phenomenon, but I can
see no other explanation. This kind of interaction is frequent between moving bodies, for example through tidal effect.
Restarting from this questionable answer, I have been wondering whether it can occur within a structure of clouds with asymmetries, initially at rest, both internally and with respect to each other.
What follows is intuitive and speculative, as I do not know how to deal with the problem mathematically.
My own idea of how it could occur, very intuitively and informally, is that when two clouds are both collapsing to their own
centers of mass, gravitational attraction of cloud A will slow down
the collapse of the closest parts of cloud B (and conversely), so that
the center of mass will move, and the the velocity of the collapsing cloud
components going no longer through the center of mass, they have
acquired angular momentum with respect to that center of mass, which does initiate the spining. Then
indeed, the collapse will increase the spin. The symmetry of the
phenomenon with respect to the median plane (assuming symmetrical
clouds to simplify) applies also to the angular momenta induced in
each cloud, so that they get opposite angular momenta, and opposite spin.
So all you need to get started would be inhomogeneity in a motionless cosmic cloud, that lead to collapse of subparts to their center of mass, while being distorted by neigboring subparts. This create spin, from which we get higher speeds as the cloud parts keep collapsing.
This is my own intuitive reconstruction. Hence do not trust me unless it is confirmed by professionals. My problem is finding one who would address/answer this question
A: There is an angular momentum problem with regard to star formation, but you have the sense of the problem completely backwards. The problem is not where the angular momentum arises. The problem is where does it go.
Gas clouds a tenth of a parsec across have been routinely been observed to rotate at about one revolution every five or ten million years or so ($\Omega \approx 3\times10^{-14}$ radians/second). That's about 30 or 40 times faster than the mean galactic rotation rate. Those interstellar gas clouds interact gravitationally with one another and with nearby stars. The gravity gradient torque across a tenth of a parsec exerted by a nearby gas cloud or star can easily build up that tiny rotation rate.
That rotation rate sounds tiny, but it's not. Were the entire gas cloud to shrink to a star and conserve angular momentum along the way, the star would necessarily be spinning at about two revolutions per minute. The star could not form! This is the crux of the angular momentum problem.
The old nebular hypothesis (from the mid 18th century) regarding the formation of the solar system had huge problems with angular momentum, so huge the theory was discarded. The revived version of the hypothesis (1970s) is now the dominant theory regarding star and planetary formation because it has solved the angular momentum problem to some extent. The solution isn't complete; some problems with angular momentum remain. "Where does it go?" remains a partially unanswered question.
A: You could start from the premise that there was not net angular momentum in the universe at all; but it would still be the case that everything of interest was spinning.
On the scales of stars and planets there are (at least) two important mechanisms that result in individual systems having angular momentum. The first is turbulence. If you take a parcel of turbulent gas from a giant molecular cloud it will always possess some angular momentum, even if the total cloud does not. As the parcel collapses to form a star/planets... I'm not repeating all this.
Second, stars form in clusters. There is interaction between stellar systems early in their lives. Again, the cluster may have little net J, but groups of stars can, relative to their own centre of mass frame.
On bigger scales (not my field) I think the second of these explanations becomes more important. The interaction and accretion of galaxies is what gives individual galaxies a spin, even if the clusters they are born in have much less or even no net J.
Edit: As an example of how turbulent velocity fields lead to gravitational condensations containing angular momentum you could do worse than study the star formation simulation performed by Matthew Bate and collaborators. These simulations start off in clouds with zero net angular momentum, yet produce a host of stars with swirling accretion disks, binary systems of all shape and sizes etc. An example journal paper can be found here: http://adsabs.harvard.edu/abs/2009MNRAS.392..590B  Here is a web page where you can download the animations and study them at length  http://www.astro.ex.ac.uk/people/mbate/Cluster/cluster500RT.html
Turbulent clouds are by their nature random and stochastic in terms of their motions. Often the velocity field is defined in terms of a power law dependence on spatial scale. The formation of vortices is a characteristic of turbulent media. They can be produced in the absence of external forces. The vortices contain angular momentum.
A: If you take an air filled rubber ball and try to squash it equally from all sides it is too hard. Twisting the ball either way seems easier to deform it. So perhaps a collapse of lighter material into the gravitation pull of the denser core becomes a vortex because it is the easiest path of momentum to the core. Where friction increases as the material gets denser towards the centre, considering the speed of collapse is faster furtherest from the core, its momentum as it collides with denser material closer to the core it is symptomatically deflected until the whole process becomes a vortex causing angular momentum. It seems that black hole starts rotating from the angular momentum of the material it feeds from. 
