Since their discovery almost one century ago, sleep spindles, 0.5-2s long bursts of oscillatory activity at 9-16Hz during NREM sleep, have been thought to be global and relatively uniform throughout the cortex. Recent work, however, has brought this concept into question but it remains unclear to what degree spindles are global or local and if their properties are uniform or location-dependent. We addressed this question by recording sleep in eight patients undergoing evaluation for epilepsy with intracranial electrocorticography, which combines high spatial resolution with extensive cortical coverage. We find that spindle characteristics are not uniform but are strongly influenced by the underlying cortical regions, particularly for spindle density and fundamental frequency. We observe both highly isolated and spatially distributed spindles, but in highly skewed proportions: while most spindles are restricted to one or very few recording channels at any given time, there are spindles that occur over widespread areas, often involving lateral prefrontal cortices and superior temporal gyri. Their co-occurrence is affected by a subtle but significant propagation of spindles from the superior prefrontal regions and the temporal cortices towards the orbitofrontal cortex. This work provides a brain-wide characterization of sleep spindles as mostly local graphoelements with heterogeneous characteristics that depend on the underlying cortical area. We propose that the combination of local characteristics and global organization reflects the dual properties of the thalamo-cortical generators and provides a flexible framework to support the many functions ascribed to sleep in general and spindles specifically.