Recent experiments [Nakata, M. et al., End-to-end stacking and liquid crystal condensation of 6 to 20 basepair DNA duplexes. Science 2007; 318:1276-1279] have demonstrated spontaneous end-to-end association of short duplex DNA fragments into long rod-like structures. By means of extensive all-atom molecular dynamic simulations, we characterized end-to-end interactions of duplex DNA, quantitatively describing the forces, free energy and kinetics of the end-to-end association process. We found short DNA duplexes to spontaneously aggregate end-to-end when axially aligned in a small volume of monovalent electrolyte. It was observed that electrostatic repulsion of 5'-phosphoryl groups promoted the formation of aggregates in a conformation similar to the B-form DNA double helix. Application of an external force revealed that rupture of the end-to-end assembly occurs by the shearing of the terminal base pairs. The standard binding free energy and the kinetic rates of end-to-end association and dissociation processes were estimated using two complementary methods: umbrella sampling simulations of two DNA fragments and direct observation of the aggregation process in a system containing 458 DNA fragments. We found the end-to-end force to be short range, attractive, hydrophobic and only weakly dependent on the ion concentration. The relation between the stacking free energy and end-to-end attraction is discussed as well as possible roles of the end-to-end interaction in biological and nanotechnological systems.