The most common equation for the self ionization of water I've seen is with protons and hydroxyl ions as products.
H2O ⇌ H+ + OH-
I've also seen the following equation with hydronium ions as a product instead of protons
2H2O ⇌ H3O+ + OH-
Does the first equation actually happen, or is it just an abbreviation for the second? Or do both species (hydronium and protons) exist in solution, or something more complicated?