Iridates are characterized by a fascinating interplay of spin-orbit and electron-electron interactions. The honeycomb-lattice materials A(2)IrO(3) (A = Na,Li) have been proposed to realize pseudospin-1/2 Mott insulating states with strongly anisotropic exchange interactions, described by the Heisenberg-Kitaev model, but other scenarios involving longer-range exchange interactions or more delocalized electrons have been put forward as well. Here we study the influence of nonmagnetic doping, i.e., depleted moments, on the magnetic properties of experimentally relevant variants of the Heisenberg-Kitaev and Heisenberg J(1)-J(2)-J(3) models. We generically find that the zigzag order of the clean system is replaced, upon doping, by a spin-glass state with short-ranged zigzag correlations. We determine the spin-glass temperature as a function of the doping level and show that this quantity allows one to assess the importance of longer-range exchange interactions when the doping is driven across the site-percolation threshold of the honeycomb lattice.DFGHelmholtz associationFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Tech Univ Dresden, Inst Theoret Phys, D-01062 Dresden, GermanyUniv Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, BrazilUniv Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, BrazilDFGFOR 960DFGGRK 1621Helmholtz associationVI-521