Understanding water transport by the subducting slab and the corner flow of the mantle wedge is a crucial topic because it is a prime control on seismic tremors, arc-to-intraplate volcanoes as well as on global water distribution in the mantle. However, most of previous studies focused on water transport by the subducting slab and did not quantitatively evaluated the amount of water carried by the corner flow into the deep mantle. Using two-dimensional numerical experiments, we model both the dehydration of the subducting slab and (de)hydration of the mantle wedge and quantify the amount of water transported by both of them. We use the water solubilities of basalt and peridotite derived from laboratory measurements and from thermodynamic calculations, and compare the implications of their differences. Our calculations show that the two models for the water solubilities of basalt result in either abundant or scarce free water through extensive or negligible dehydration of the sub-forearc oceanic crust, leading to a hydrated or a dry cold nose of the mantle wedge, respectively. Further, the oceanic crust of the subducting slab is almost dehydrated prior to reaching a depth of 250 km, regardless of subduction parameters and the models for the water solubilities of basalt. The dehydration depth of the lithospheric mantle of the subducting slab deepens with decreasing slab temperature. The lithospheric mantle of cold subducting slab (e.g., Northeast Japan) experiences partial dehydration at sub-backarc depths and transports the remaining bound water beyond a depth of 250 km, regardless of the models for the water solubilities of peridotite. Deep water transport by the corner flow of the mantle wedge is negligible regardless of the models for the water solubilities of peridotite. The water carried by the lithospheric mantle may be the cause of backarc and intraplate volcanoes in Northeast Asia.