Remote sensing enables the quantification of tropical deforestation with high spatial resolution^,. This in-depth mapping has led to substantial advances in the analysis of continent-wide fragmentation of tropical forests^,,,. Here we identified approximately 130 million forest fragments in three continents that show surprisingly similar power-law size and perimeter distributions as well as fractal dimensions. Power-law distributions^,, have been observed in many natural phenomena^, such as wildfires, landslides and earthquakes. The principles of percolation theory^,, provide one explanation for the observed patterns, and suggest that forest fragmentation is close to the critical point of percolation; simulation modelling also supports this hypothesis. The observed patterns emerge not only from random deforestation, which can be described by percolation theory^,, but also from a wide range of deforestation and forest-recovery regimes. Our models predict that additional forest loss will result in a large increase in the total number of forest fragments—at maximum by a factor of 33 over 50 years—as well as a decrease in their size, and that these consequences could be partly mitigated by reforestation and forest protection.