  It is shown that the foundational axioms of MOND alone predict a strong
correlation between a bulk measure of the baryonic surface density, $\Sigma_B$,
and the corresponding dynamical one, $\Sigma_D$, of an isolated object, such as
a galaxy. The correlation is encapsulated by its high- and low-$\Sigma_B$
behaviors. For $\Sigma_B\gg\Sigma_M\equiv a_0/2\pi G$ ($\Sigma_M$ is the
critical MOND surface density) one has $\Sigma_D\approx\Sigma_B$. Their
difference -- which would be interpreted as the contribution of dark matter --
is $\Sigma_P=\Sigma_D-\Sigma_B\sim\Sigma_M\ll\Sigma_B$. In the deep-MOND limit,
$\Sigma_B\ll\Sigma_M$, one has $\Sigma_D\sim (\Sigma_M\Sigma_B)^{1/2}$. This is
a primary prediction of MOND, shared by all theories that embody its basic
tenets. Sharper correlations, even strict algebraic relations,
$\Sigma_D(\Sigma_B)$, are predicted in specific MOND theories, for specific
classes of mass distribution -- e.g., pure discs, or spherical systems -- and
for specific definitions of the surface densities. I proceed to discuss such
tighter correlations for the central surface densities of axisymmetric galactic
systems, $\Sigma^0_B$ and $\Sigma^0_D$. Past work has demonstrated such
relations for pure discs in the AQUAL and QUMOND theories. Here I consider them
in broader classes of MOND theories. For most observed systems, $\Sigma^0_D$
can not be determined directly at present, but, in many cases, a good proxy for
it is the acceleration integral $\mathcal{G}\equiv\int_0^\infty g_r d\ln~r$,
where $g_r$ is the radial acceleration along a reflection-symmetry plane of a
system, such as a disc galaxy. $\mathcal{G}$ can be determined directly from
the rotation curve. I discuss the extent to which $\mathcal{G}$ is a good proxy
for $\Sigma^0_D$, and how the relation between them depends on system geometry,
from pure discs, through disc-plus-bulge ones, to quasi-spherical systems.
