Using tools from asymptotic analysis for elliptic equations, we study in this work the hemodynamics in a stented artery connected either to a collateral artery or to an aneurysmal sac. The blood ow is driven by a pressure drop. Our aim is to characterize the ow-rate and the pressure in the contiguous zone to the main artery: using boundary layer theory we construct a homogenized first order approximation with respect to epsilon, the size of the stent's wires. In the collateral artery this gives the flow-rate. In the case of the aneurysm, it shows that : (i) the zeroth order term of the pressure in the sac equals the averaged pressure along the stent in the main artery, (ii) the presence of the stent inverses the rotation of the vortex. We derive new averaged implicit interface conditions that our approxima- tion formally satisfies, generalizing our analysis to other possible geometrical configurations. In the last part we provide 2D numerical results that illustrate and validate the theoretical approach and we show a possible strategy to tackle the case of a realistic full-3D geometry for which no direct simulation is possible.