Many different hypotheses on the molecular mechanisms of vesicle fusion exist. Because these mechanisms cannot be readily asserted experimentally, we address the problem by a coarse-grained molecular dynamics simulations study and compare the results with the results of other techniques. The simulations performed include the fusion of small and large vesicles and exocytosis, i.e., the fusion of small vesicles with flat bilayers. We demonstrate that the stalk, the initial contact between two fusing vesicles, is initiated by lipid tails that extend spontaneously. The stalk is revealed to be composed of the contacting monolayers only, yet without hydrophobic voids. Anisotropic and radial expansion of the stalk have been theorized; we show that stalk evolution can proceed via both pathways starting from similar setups and that water triggers the transition from elongated stalk to hemifusion diaphragm.