Re: What is the mechanism by which a field spreads.

What you see "spreading" are the force lines of 
a static magnetic field. You can also see similar
"spreading" phenomenon in the graph of force lines
for a static electric field.

The force lines are drawn according to two rules:
1. the tangent of the curve is parallel to the
direction of the electric or magnetic field
2. the density of the curves is proportional to
the intensity of the electric field or magnetic
field

However, it's hard to define the "density" for
the force lines. Therefore the graph of force
lines are generally just conceptual illustrations.

The magnetic field of a permanent magnet is caused
by magnetic dipole of unpaired electrons in that
magnet. The magnetic field of a magnetic dipole
can be calculated by using
 http://www.treasure-troves.com/physics/MagneticDipole.html

There are a lot of magnetic dipoles in a magnet. If
their positions and orientations are already known,
we can calculate the magnetic field generated by
them separately and then sum them up to obtain the
magnetic field generated by the whole magnet.

Therefore, it's the distribution of magnetic dipoles
in a magnet which determines the magnetic field. By
breaking a magnet into small pieces and rearranging 
them, you can even "design" a magnetic field.