Stars can be consumed (either tidally disrupted or swallowed whole) by massive black holes (MBHs) at galactic centers when they move into the vicinity of the MBHs. In this study, we investigate the rates of stellar consumption by central MBHs and their cosmic distributions, including the effects of triaxial galaxy shapes in enhancing the reservoir of low-angular-momentum stars and incorporating realistic galaxy distributions. We find that the enhancement in the stellar consumption rates due to triaxial galaxy shapes can be significant, by a factor of ~3 for MBH mass $M_{rm BH}sim10^5$-$10^6$Msun and up to more than one order of magnitude for $M_{rm BH}gtrsim10^8$Msun. Only for $M_{rm BH}lesssim10^7$Msun are the stellar consumption rates significantly higher in galaxies with steeper inner surface brightness profiles. The average (per galaxy) stellar consumption rates correlate with central MBH masses positively for $M_{rm BH}gtrsim10^7$Msun and negatively for $M_{rm BH}lesssim10^7$Msun. The volumetric stellar tidal disruption rates are ~$3times10^{-5}$/yr/Mpc$^3$ for MBHs in the mass range of $10^5$-$10^8$Msun at z=0; and the volumetric stellar consumption rates by MBHs with higher masses are ~$10^{-6}$/yr/Mpc$^3$, which can be the stellar tidal disruption rate if the high-mass BHs are extremely spinning Kerr BHs or the rate of being swallowed if those BHs are Schwarzschild ones. The volumetric stellar consumption rates decrease with increasing redshift, and the decrease is relatively mild for $M_{rm BH}sim10^5$-$10^7$Msun and stronger for higher $M_{rm BH}$. Most of the stellar tidal disruption events (TDEs) at z=0 occur in galaxies with mass $M_{rm gal}lesssim10^{11}$Msun, and about 1%-2% of the TDEs can occur in high-mass galaxies with $M_{rm gal}gtrsim10^{11}$Msun.
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