ABSTRACTWhat determines the nuclear radio emission in local galaxies? To address this question, we combine optical [O iii] line emission, robust black hole (BH) mass estimates, and high-resolution e-MERLIN 1.5-GHz data, from the LeMMINGs survey, of a statistically complete sample of 280 nearby optically active (LINER and Seyfert) and inactive [H ii and absorption line galaxies (ALGs)] galaxies. Using [O iii] luminosity ($L_{\rm [O\, \small {III}]}$) as a proxy for the accretion power, local galaxies follow distinct sequences in the optical–radio planes of BH activity, which suggest different origins of the nuclear radio emission for the optical classes. The 1.5-GHz radio luminosity of their parsec-scale cores (Lcore) is found to scale with BH mass (MBH) and [O iii] luminosity. Below MBH ∼ 106.5 M⊙, stellar processes from non-jetted H ii galaxies dominate with $L_{\rm core} \propto M_{\rm BH}^{0.61\pm 0.33}$ and $L_{\rm core} \propto L_{\rm [O\, \small {III}]}^{0.79\pm 0.30}$. Above MBH ∼ 106.5 M⊙, accretion-driven processes dominate with $L_{\rm core} \propto M_{\rm BH}^{1.5-1.65}$ and $L_{\rm core} \propto L_{\rm [O\, \small {III}]}^{0.99-1.31}$ for active galaxies: radio-quiet/loud LINERs, Seyferts, and jetted H ii galaxies always display (although low) signatures of radio-emitting BH activity, with $L_{\rm 1.5\, GHz}\gtrsim 10^{19.8}$ W Hz−1 and MBH ≳ 107 M⊙, on a broad range of Eddington-scaled accretion rates ($\dot{m}$). Radio-quiet and radio-loud LINERs are powered by low-$\dot{m}$ discs launching sub-relativistic and relativistic jets, respectively. Low-power slow jets and disc/corona winds from moderately high to high-$\dot{m}$ discs account for the compact and edge-brightened jets of Seyferts, respectively. Jetted H ii galaxies may host weakly active BHs. Fuel-starved BHs and recurrent activity account for ALG properties. In conclusion, specific accretion–ejection states of active BHs determine the radio production and the optical classification of local active galaxies.