  We study the intrinsic large-scale distribution and evolution of seven
ionized metals in the IllustrisTNG magneto-hydrodynamical cosmological
simulation. We focus on the fractions of C\,\textsc{ii}, C\,\textsc{iv},
Mg\,\textsc{ii}, N\,\textsc{v}, Ne\,\textsc{viii}, O\,\textsc{vi}, and
Si\,\textsc{iv} in different cosmic web structures (filaments, haloes, and
voids) and gas phases (warm-hot intergalactic medium WHIM, hot, diffuse, and
condensed gas) from $z=6$ to $z=0$. Our analysis provides a new perspective to
the study of the distribution and evolution of baryons across cosmic time while
offering new hints in the context of the well-known missing baryons problem.
The cosmic web components are here identified using the local comoving dark
matter density, which provides a simple but effective way of mapping baryons on
large scales. Our results show that C\,\textsc{ii} and Mg\,\textsc{ii} are
mostly located in condensed gas inside haloes in high-density and
low-temperature star-forming regions ($\rho_{\rm gas}/\bar{\rho}_{\rm
bar}\gtrsim10^3$, and ${\rm T}\lesssim10^{5}$~K). C\,\textsc{iv} and
Si\,\textsc{iv} present similar evolution of their mass fractions in haloes and
filaments across cosmic time. In particular, their mass budgets in haloes in
condensed phase ($\rho_{\rm gas}/\bar{\rho}_{\rm bar}\gtrsim10^3$, and ${\rm
T}\lesssim10^{5}$~K) are driven by gas cooling and star formation with a peak
at $z\sim2$. Finally, our results confirm that O\,\textsc{vi},
Ne\,\textsc{viii}, and N\,\textsc{v} are good tracers of warm/hot and
low-density gas at low redshift ($\rho_{\rm gas}/\bar{\rho}_{\rm
bar}\lesssim10^3$, and ${\rm T}\gtrsim10^{5}$~K), regions that are likely to
contain most of the missing baryons in the local Universe.
