  This article constitutes the final and main part of a three-paper sequence,
whose goal is to prove global well-posedness and scattering of the energy
critical Maxwell-Klein-Gordon equation (MKG) on $\mathbb{R}^{1+4}$ for
arbitrary finite energy initial data. Using the successively stronger
continuation/scattering criteria established in the previous two papers, we
carry out a blow-up analysis and deduce that the failure of global
well-posedness and scattering implies the existence of a nontrivial stationary
or self-similar solution to MKG. Then, by establishing that such solutions do
not exist, we complete the proof.
