||Sea-surface temperature images of the coastal upwelling regions off Northwest Africa show that the core of upwelling is sometimes located far from the coast. This has been documented in three regions that share a common feature, namely a wide and shallow continental shelf. This upwelling feature plays a key role in the ecology of the Canary Current System. It creates an innerfront which provides retention for biological material, e.g. fish eggs and larvae, in the highly productive nearshore environment. An analytical model has been developed based on a two dimensional extension of Ekman's solution. The linear and steady response of a homogeneous ocean forced by an upwelling-favorable wind provides a mechanism for the upwelling separation from the coast. The merging of the surface and bottom Ekman layers induces a very weak cross-shore circulation and a "kinematic barrier" for the Ekman transport divergence. In the case of an alongshore wind, the barrier is located near the isobath h ≈ 0.4D, where D is the thickness of Ekman layers. This yields an upwelling cell which is essentially concentrated in the region 0.5D < h < 1.25D, with upwelling occurring preferentially near the isobath h ≈ 0.6D. It turns out that the cross-shore width of upwelling scales with D/S, the ratio of Ekman depth to bottom topographic slope. The application of this solution to real bathymetric profiles rationalizes, not only the offshore upwelling observations in Northwest Africa, but also the influence of topography on the cross-shelf structure of a wind-driven coastal upwelling. The model also quantifies the effect of the cross-shore wind component showing how it drives the nearshore pressure gradient adjustment and how it affects the upwelling. A linear numerical experiment reproduces the theoretical steady solution, thereby allowing investigation of the transient regime. Relaxation of the hypothesis in the numerical model validates the linear assumption of the theory and then allows investigation of the sensitivity to friction parameterizations and the influence of stratification. The latter leads to an "oscillation" of the upwelling cell with seaward migration driven by outcropping and homogeneization of the water column, and, coastal incursion driven by a "boundary layers splitting" process caused by shoreward advection of the isopycnal dome and stratification of the inner shelf.