The time-like transition form factors of the $\pi^0$, $\eta$ and $\eta^\prime$ pseudoscalar mesons are predicted by means of different fits to existing experimental data on their space-like counterparts using Padé approximants. As a byproduct, we calculate the integrated branching ratios of the single Dalitz decays $\pi^0\to e^+e^-\gamma$ and $\eta^{(\prime)}\to\ell^+\ell^-\gamma$, with $\ell=e$ or $\mu$, and the double Dalitz decays $\pi^0\to e^+e^-e^+e^-$ and $\eta^{(\prime)}\to\ell^+\ell^-\ell^+\ell^-$.