In this paper we give exact or almost exact bounds for the continuous gathering problem on grids. Under very general hypothesis on the traffic demand, we mainly prove that the throughput is determined by the bottleneck around the base station. We deal with two cases: the base station located in the center and in the corner. We use dual lower bounds and describe a protocol which is optimal when the traffic is uniform., OPTx-editorial-board=yes, OPTx-proceedings=yes, OPTx-international-audience=no