The time dependence of the domain switching current density, Jsw(t), under pulsed voltages on a ferroelectric parallel-plate capacitor is the consequence of region-by-region polarization reversals across the film. As the distributive coercive voltage of domain nucleation increases from zero to the maximum applied voltage during the capacitor charging time, Jsw(t) is proportional to the domain switching speed at each time. By transforming the spatially inhomogeneous domain nucleation distribution into a temporal distribution of coercive fields (Ec), a local lnJsw versus Ec-1 plot is derived for each domain, following the Merz equation. This provides insight into the independent domain switching dynamics at different nucleation sites in Pb(Zr0.35Ti0.65)O3 thick films over a large current range. Although the activation field of the slope of the lnJsw(t) versus Ec-1 plot varies with film area and temperature, all the plots extrapolate to a single point (J0, E0) from which the ultimate domain switching current density of J0 =1.4 x 108 A cm-2 at the highest field of E0 = 0.20-0.25 MV cm-1 is derived. Unexpectedly, J0 and E0 are independent of the film thickness and area, after correction for a small interfacial-layer effect. This analysis provides rigorous evidence for nucleation rate-limited domain switching with a subpicosecond nucleation time and the relative unimportance of domain forward-growth time across film thicknesses between 0.14 and 2 mu m. This work paves the way to improve the efficiency of ferroelectric thick-film functionality in electronic and optoelectronic devices with ultrafast clock rates.