The aim is to compare the geomorphometric signatures of catchment basins (Steepest descent lines converging to outlets SDO) and mountain ranges (Steepest ascent lines toward summits SATS) on a set islands in various topographical, geological and morphoclimatic settings: Lesvos (1656 km2, 39.51°N, max elevation 903 meters), Kerguelen (6761 km2, 49.19°S, 1792 m), Crete (8325 km2, 35.31°N, 2442 m), Cyprus (9230 km2, 35.13°N, 1971 m), 4205 m), New-Caledonia (16,469 km2, 21.24°S, 1621 m), Formosa (35,901 km2, 23.6°N, 3917 m), and Sri Lanka (66,375 km2, 7.87°N, 2518 m). The SATS resulting patches corresponds to the dual partitioning of SDO. For comparative purpose, the same SRTM 3 arc second DTM is used. While the SDO basin tessellation depends mostly of hydrological processes, the dual fragmentations given by the SATS are conversely more related to the lithology and the tectonic of mountainous areas. The main hypothesis is that there are relationships between environmental factors and pattern signatures for both catchment basins and mountain ranges. The tessellation of catchment basins uses the D8 steepest descent method available in most GIS toolboxes. On the other hand, an ad hoc stepwise algorithm (MAPAM) delineate elementary hills up to the major mountain ranges associated with highest summits. The outcome of merging SDO and SATS is a combined tessellations which tiles are landform units (LU2s) collecting water from the same slope pouring down the same watershed (Water divide, crest line) and collected by the same section of river (Talweg) between two confluences. The statistical textural properties of the tiles are analyze for both SDO and SATS tessellations and resulting LU2s combined pattern and com-pared on the seven islands with the area-number method also called “Korčak Number-Area law.” The size distributions of Korcak law for both catchment basins (SDO) and mountain ranges (SATS) is best fitted with power law functions N = α·A–β. On top of morphogenic climatic factors, the parameter β differs from one geological context to another. Coupled with other geostatistical approach of land or bathymetric surface depictions (i.e., variograms, geomorphometry, etc.), this combined SDO and SATS tessellation analysis contribute to innovative semi-automatic survey and mapping methods for a wide range of environmental applications, for instance topographical habitats, distributed hydrological modeling, geomorphologic risk assessment and transportation planning optimization.