We study with Angle Resolved PhotoElectron Spectroscopy (ARPES) the evolution of the electronic structure of Sr2IrO4, when holes or electrons are introduced, through Rh or La substitutions. At low dopings, the added carriers occupy the first available states, at bottom or top of the gap, revealing an asymmetric gap of 0.7eV, in good agreement with STM measurements. At further doping, we observe a reduction of the gap and a transfer of spectral weight across the gap, although the quasiparticle weight remains very small. We discuss the origin of the in-gap spectral weight as a local distribution of gap values.PACS numbers: 71.30.-h, 71.27.-a, 79.60.-i The reaction of an insulator to doping can reveal many things on its underlying structure. For a band insulator, a simple shift of the chemical potential into bands that were previously completely filled or empty can be expected. If more complex electronic correlations are involved, the formation of in-gap states and/or large transfer of spectral weight across the gap could occur 1,2 . This problem received a lot of attention in the case of cuprates 3,4 . It is very interesting to investigate this in Sr 2 IrO 4 , whose insulating nature is not completely understood. The idea driving the field for a few years is that strong spin-orbit coupling reshapes the electronic structure in a way that enhances correlations 5 . Especially, a narrow half-filled band of J=1/2 character forms at the Fermi level, which could be split by correlations to form a Mott insulator. The exact role of the antiferromagnetic (AF) ordering observed below 240 K 6 in the insulating nature is still debated 7,8 . On the other hand, applying pressure, even up to 55 GPa, was not able to close the gap 9 , which is surprising for a Mott insulator. In this context, it would be interesting to know more about the electronic structure of doped phases, which exhibit metallic-like behaviors even for rather low doping rates 10-13 .Recently, a few Angle Resolved Photoemission (ARPES) studies of doped iridate phases were reported, but they lead to quite a confusing picture. For Rh substitutions, which results in effective hole doping 13 , a metallic-like state was observed, albeit with residual pseudogaps instead of well defined quasiparticles (QP) peaks 14 . Another kind of metallic state was observed by evaporating K on the surface of Sr 2 IrO 4 , which presumably dopes electrons into it 15 . In this case, well defined QP were observed, with strong momentum and temperature dependences that resemble those found in the cuprates and even possible signs of superconductivity 16,17 . Very recently, results similar to intermediate K coverage were reproduced in La doped Sr 2 IrO 4 18 . In these cases, a large Fermi Surface (FS) containing ∼ 1±x electrons was apparently observed (x is the number of added carriers), although the spectral weight along it could be strongly modulated. In contrast, La doping in Sr 3 Ir 2 O 7 apparently produces a small FS containing only the added x electrons 19 with a progressive reduct...