  We extract the leading Fock-state light front wave functions (LF-LFWFs) of
both the light and heavy pseudoscalar mesons, e.g., the pion (at masses of 130
MeV, 310 MeV and 690 MeV), $\eta_c$ and $\eta_b$, from their covariant
Bethe-Salpeter wave functions within the rainbow-ladder (RL) truncation. It is
shown that the LF-LFWFs get narrower in $x$ (the longitudinal momentum fraction
of meson carried by the quark) with the increasing current quark mass, and the
leading twist parton distribution amplitudes (PDAs) inherit this feature.
Meanwhile, we find in the pion the LF-LFWFs only contribute around 30\% to the
total Fock-state normalization, indicating the presence of significant higher
Fock-states within. In contrast, in the $\eta_c$ and $\eta_b$ the LF-LFWFs
contribute more than $90$\%, suggesting the $Q\bar{Q}$ valence Fock-state
truncation as a good approximation for heavy mesons. We thus study the
3-dimensional parton distributions of the $\eta_c$ and $\eta_b$ with the
unpolarized generalized parton distribution function (GPD) and the transverse
momentum dependent parton distribution function (TMD). Through the
gravitational form factors in connection with the GPD, the mass radii of the
$\eta_c$ and $\eta_b$ in the light-cone frame are determined to be $r_{E,{\rm
LC}}^{\eta_c} =0.150$ fm and $r_{E,{\rm LC}}^{\eta_b} =0.089$ fm respectively.
