Classical capillarity theory is based on the study of volume-constrained critical points and local/global minimizers of the Gauss free energy of a liquid droplet occupying a region inside a container. \In 2016 Maggi and Valdinoci introduced a family of nonlocal capillarity models where surface tension energies are replaced with fractional interaction energies. \I will discuss a nonlocal capillarity problem involving kernels which are possibly anisotropic and have different homogeneity in order to take into account the possibility that the liquid/air interaction and the liquid/surface one are different.