(N/A) $(i)$ The nature of the material being electrolysed.
$(ii)$ The type of electrodes used: If the electrode is inert (e.g.,$Pt$ or $Au$),it does not participate in the reaction. If the electrode is reactive,it participates in the electrode reaction.
$(iii)$ The standard electrode potentials of the species present: Species with a higher $E^{\circ}$ value are reduced at the cathode,and species with a lower $E^{\circ}$ value are oxidized at the anode.
Example: In the electrolysis of aqueous $NaCl$ with inert electrodes,$H_{2}O$ is reduced at the cathode instead of $Na^{+}$ because $H_{2}O$ has a higher reduction potential.
$(iv)$ The concentration of the electrolyte: According to the Nernst equation,changes in concentration affect the electrode potential,which can alter the products.
Example: In the electrolysis of dilute $H_{2}SO_{4}$,water is oxidized to $O_{2}$. However,in highly concentrated $H_{2}SO_{4}$,$SO_{4}^{2-}$ ions are oxidized to $S_{2}O_{8}^{2-}$ according to the reaction: $2SO_{4}^{2-} \rightarrow S_{2}O_{8}^{2-} + 2e^{-}$.