We study the adhesion of an elastic sheet on a rigid spherical substrate. Gauss'Theorema Egregium shows that this operation necessarily generates metric distortions (i.e. stretching) as well as bending. As a result, a large variety of contact patterns ranging from simple disks to complex branched shapes are observed as a function of both geometrical and material properties. We describe these different morphologies as a function of two non-dimensional parameters comparing respectively bending and stretching energies to adhesion. A complete configuration diagram is finally proposed.Different types of projections have been developed to map the earth, such as the Mercator projection [1] widely used for navigation purposes. Cartographers creating these projections face the challenge to transform a sphere into a planar region. However Gauss proved in his Theorema Egregium that such an operation cannot preserve both areas and angles. Indeed the product of the principal curvatures is constant under local isometry [2]. In other words, Gauss' theorem states that it is impossible to flatten a tangerine peel without tearing it. As a consequence, the length scale on a Mercator conformal map (which does preserve the angles) depends on the latitude. Sailors searching for the shortest route to cross the oceans thus follow curved paths on such maps. From a technological point of view, covering a curved substrate with a flexible surface is however a common operation. For instance, placing a contact lens over an eye of a mismatched geometry induces stresses in lenses [3] and wrapping a sphere with a flat paper generates wrinkles [4]. As a practical consequence, bandages dedicated to knuckles or nose are tailored into specific templates in order to provide a good adhesion on round body parts [5]. Understanding the adhesion of vesicles on curved substrates is also crucial for some drug delivery applications [6]. In the field of microtechnology, special processes for depositing thin films [7] or components [8] on curved substrates have been developed especially to account for the geometrical constraints dictated by Gauss'Theorema Egregium. New theoretical approaches have also been recently developed to account for the specific crystallographic properties of crystals lying on curved substrates [9]. The contact between a graphene sheet and a corrugated soft substrate finally allows to estimate the adhesion energy and bending stiffness of the graphene sheet [10], which leads to novel metrology techniques.We propose to study, through model experiments, the reciprocal problem of the cartographer, i.e. transforming a planar elastic sheet into a portion of sphere. A thin film is deposited on a rigid spherical cap coated with a thin liquid layer (Fig. 1a). Surface tension promotes the contact between the film and the sphere, which reduces the liquid/air interfacial energy at the cost of bending In this example the region in contact with the sphere (contact zone) forms branched wavy patterns, while the unstuck parts of the sheet do not touch ...