It has been recently suggested that moderate and large earthquakes can be triggered by similarly sized events at very long range. Here we study the main characteristics of earthquake triggering by determining its correlation length, time dependence, and directionality. The problem is examined at a global level, by using the Harvard centroid moment tensor catalogue. Our results show that the correlation lengths depend only weakly on the magnitude thresholds involved. No significant systematic triggering is observed for distances greater than the lithospheric thickness (100--150 km), and the correlation length magnitude is similar to the seismogenic thickness (10--20 km). The mean triggering distance and correlation length both increase with time very slowly compared with what would be expected from a normal diffusion process. This is consistent with a clock advance on the failure time based on the constitutive rules for subcritical crack growth following a transient change in the loading stress. The power law scaling disappears after a few months. A functional form for the probability of triggering as a function of time and distance is proposed on the basis of the properties of near critical point systems. The model fits the data well and could be used to calculate conditional probabilities for time-dependent seismic hazard due to earthquake triggering. An apparent directionality effect that was observed in the data set can be attributed to an artefact of poor depth determination. These results do not preclude individual long-range triggering with a potential directionality effect, but they do rule out a statistical correlation at distances much greater than the thickness of the lithosphere.