Size frequency distributions of canopy gaps are a hallmark of forest dynamics. But it remains unknown whether legacies of forest disturbance are influencing vertical size structure of landscapes, or space-filling in the canopy volume. We used data from LiDAR remote sensing to quantify distributions of canopy height and sizes of 434 501 canopy gaps in five tropical rain forest landscapes in Costa Rica and Hawaii. The sites represented a wide range of variation in structure and natural disturbance history, from canopy gap dynamics in lowland Costa Rica and Hawaii, to stages and types of stand-level dieback on upland Mauna Kea and Kohala volcanoes. Large differences in vertical canopy structure characterized these five tropical rain forest landscapes, some of which were related to known disturbance events. Although there were quantitative differences in the values of scaling exponents within and among sites, size frequency distributions of canopy gaps followed power laws at all sites and in all canopy height classes. Scaling relationships in gap size at different heights in the canopy were qualitatively similar at all sites, revealing a remarkable similarity despite clearly defined differences in species composition and modes of prevailing disturbance. These findings indicate that power-law gap-size frequency distributions are ubiquitous features of these five tropical rain forest landscapes, and suggest that mechanisms of forest disturbance may be secondary to other processes in determining vertical and horizontal size structure in canopies.