Previous adhesion maps, such as the JG Uohnson Greenwood) and YCG (Yao Ciavarella Gao) maps, are used to guide the selection of Bradley, DMT, M-D, JKR and Hertz models. However, when the size of the contact sphere decreases to the small scale, the applicability of JG and YCG maps is limited because the assumptions regarding the contact region profile, interaction between contact bodies and sphere shape in the classical models constituting these two maps are no longer valid. To avoid this limitation, in this paper, a new numerical model considering size effects of the sphere is established first and then introduced into the new adhesion maps together with the YGG (Yao Guduru Gao) model and Hertz model. Regimes of these models in the new map under a certain sphere radius are demarcated by the criteria related to the relative force differences and the ratio of contact radius to sphere radius. In addition, the approaches at pull-off, jump-in and jump-out for different Tabor parameters and sphere radii are provided in the new maps. Finally, to make the new maps more feasible, the numerical results of approaches, force and contact radius involved in the maps are formularized by using the piecewise fitting. (C) 2015 Elsevier Inc. All rights reserved.