  We study a dark matter (DM) model offering a very natural explanation of two
(naively unrelated) problems in cosmology: the observed relation $\Omega_{\rm
DM}\sim\Omega_{\rm visible}$ and the observed asymmetry between matter and
antimatter in the Universe, known as the "baryogenesis" problem. In this
framework, both types of matter (dark and visible) have the same QCD origin,
form at the same QCD epoch, and both proportional to one and the same
dimensional parameter of the system, $\Lambda_{\rm QCD}$, which explains how
these two, naively distinct, problems could be intimately related, and could be
solved simultaneously within the same framework. More specifically, the DM in
this model is composed by two different ingredients: the (well- studied) DM
axions and (less-studied) the quark nuggets made of matter or antimatter. The
focus of the present work is the quantitative analysis of the relation between
these two distinct components contributing to the dark sector of the theory
determined by $\Omega_{\rm DM}\equiv [\Omega_{\rm DM}(\rm nuggets)+ \Omega_{\rm
DM}(\rm axion)]$. We argue that the nugget's DM component always traces the
visible matter density, i.e. $\Omega_{\rm DM}(\rm nuggets)\sim\Omega_{\rm
visible}$ and this feature is not sensitive to the parameters of the system
such as the axion mass $m_a$ or the misalignment angle $\theta_0$. It should be
contrasted with conventional axion production mechanism due to the misalignment
when $\Omega_{\rm DM}(\rm axion)$ is highly sensitive to the axion mass $m_a$
and the initial misalignment angle $\theta_0$. We also discuss the constraints
on this model related to the inflationary scale $H_I$, non-observation of the
isocurvature perturbations, $r_T < 0.12$, and also, varies axions search
experiments.
