Exempting batteries from supplying power transients in Electric Vehicles (EVs) is beneficial to extend their useful lifespan. The adaptive capacity of High Power-density Energy Storage Systems (HPESSs) like ultracapacitors or high-speed Flywheel Energy Storage Systems (FESSs) could fulfill the targets in this context. This paper proposes a sizing/control methodology and real-time AI-based control of the storage capacity for the adaptive capacity HPESSs, used in EVs. The sizing approach consists of an optimal energy management strategy and a sizing algorithm applied to a Variable-Step HPESS (VS-HPESS). This methodology derives the battery/VS-HPESS power-split and sizes of the storage capacities. In addition, a Nonlinear Autoregressive Neural Network with eXogenous inputs (NARX-NN) is trained offline to switch the desirable capacity of the VS-HPESS in real-time operation. Finally, an experiment is designed to evaluate the proposed real-time control scheme, in which the EV power transients are emulated and applied to a dual-capacitance ultracapacitor as the VS-HPESS. The results confirm the capability of the proposed approach to meet the considered targets.