The capacity to allocate visuospatial attention is traditionally considered right-lateralized according to the effects of unilateral cerebral lesions. Contralateral hemi-spatial neglect occurs much more frequently after lesions of the right hemisphere, which has therefore been dubbed as ‘dominant’. This pattern of symptoms is supported by functional models that postulate either independence or reciprocal influences between the two hemispheres. Here we specifically explored the dependency of the right hemisphere (RH) from the left hemisphere (LH) in spatial attention. We capitalized on the well-known effect of online transcranial magnetic stimulation (TMS) on the RH in healthy individuals, consisting in transient neglect-like manifestations in the left hemi-space. We assessed whether prior stimulation of the left posterior parietal cortex with a long-lasting neuromodulatory procedure (transcranial direct current stimulation – tDCS) affected the acute effects of TMS on the right posterior parietal cortex. We performed a within-subjects factorial study with two factors: LH tDCS (sham or real) and RH TMS (sham or real), resulting in a 2×2 design. The effects on spatial attention were examined separately for the two hemi-spaces by means of a modified line-bisection task. The results indicated that TMS over the RH produced a spatial attention deficit in the left hemi-space alone and the behavioural effects of TMS were not modulated by prior stimulation of the LH. Interestingly, additional analyses showed that tDCS over the LH alone produced a deficit in spatial attention to the right hemi-space. We interpret the current results as evidence for a largely independent contribution of each hemisphere to the allocation of visuospatial attention limited to the contralateral hemi-space.