We report a new measurement of the exclusive electroproduction reaction gamma* p --> pi0 p to explore the evolution from soft non-perturbative physics to hard processes via the Q2 dependence of the magnetic (M1+), electric (E1+) and scalar (S1+) multipoles in the N --> Delta transition. 9000 differential cross section data points cover W from threshold to 1.4 GeV/c2, 4pi center-of-mass solid angle, and Q2 from 3 to 6 GeV2/c2, the highest yet achieved. It is found that the magnetic form factor GM* decreases with Q2 more steeply than the proton magnetic form factor, the ratio E1+/M1+ is small and negative, indicating strong helicity non-conservation, and the ratio S1+/M1+ is negative, while its magnitude increases with Q2.