Theoretical models of galaxy formation predict that galaxies acquire most of their baryons via cold mode accretion. Observations of high-redshift galaxies, while showing ubiquitous outflows, have so far not revealed convincing traces of the predicted cold streams, which has been interpreted as a challenge for the current models. Using high-resolution, zoom-in smooth particle hydrodynamics simulations of Lyman break galaxy (LBG) haloes combined with ionizing radiative transfer, we quantify the covering factor of the cold streams at z= 2–4. We focus specifically on Lyman limit systems (LLSs) and damped Lyα absorbers (DLAs), which can be probed by absorption spectroscopy using a background galaxy or quasar sightline, and which are closely related to low-ionization metal absorbers. We show that the covering factor of these systems is relatively small and decreases with time. At z= 2, the covering factor of DLAs within the virial radius of the simulated galaxies is ∼3 per cent (∼1 per cent within twice this projected distance), and arises principally from the galaxy itself. The corresponding values for LLSs are ∼10 and 4 per cent. Because of their small covering factor compared to the order unity covering fraction expected for galactic winds, the cold streams are naturally dominated by outflows in stacked spectra. We conclude that the existing observations are consistent with the predictions of cold mode accretion, and outline promising kinematic and chemical diagnostics to separate out the signatures of galactic accretion and feedback.