We present a model with which we predict the cross sections for the exclusive and the dissociative photo- and electroproduction of light and heavy vector mesons off protons; the model describes correctly available experimental data. The model is based on the color-dipole approach and incorporates geometric fluctuations of the target-proton partonic structure. The fluctuations are generated as randomly placed areas of high gluonic density, so-called hot spots, in the impact-parameter plane, with the number of hot spots being energy-dependent. A striking feature of the model is the prediction of a maximum of the dissociative cross section as a function of the center-of-mass energy W_{\gamma p}, followed by a steep decrease as the hot spots start to overlap with increasing energy.