The voltage controlled magnetic anisotropy (VCMA) becomes a subject of major interest for spintronics due to its promising potential outcome: fast magnetization manipulation in magnetoresistive random access memories with enhanced storage density and very low power consumption. Using a macrospin approach, we carried out a thorough analysis of the role of the VCMA on the magnetization dynamics of nanostructures with out-of-plane magnetic anisotropy. Diagrams of the magnetization switching have been computed depending on the material and experiment parameters (surface anisotropy, Gilbert damping, duration/amplitude of electric and magnetic field pulses) thus allowing predictive sets of parameters for optimum switching experiments. Two characteristic times of the trajectory of the magnetization were analyzed analytically and numerically setting a lower limit for the duration of the pulses. An interesting switching regime has been identified where the precessional reversal of magnetization does not depend on the voltage pulse duration. This represents a promising path for the magnetization control by VCMA with enhanced versatility.