Abstract. From data of the European incoherent scatter radar EISCAT, and mainly from its tristatic capabilities, statistical models of steady convection in the auroral ionosphere were achieved for various levels of magnetic activity. We propose here to consistently extend these models to the polar cap, by avoiding the use of a pre-defined convection pattern. Basically, we solve the second-order differential equation governing the polar cap convection potential with the boundary conditions provided by these models. The results display the classical twin-vortex convection pattern, with the cell centres around 17 MLT for the evening cell and largely shifted towards midnight (3–3.5 MLT) for the morning cell, both slightly moving equatorward with activity. For moderate magnetic activities, the convection flow appears approximately oriented along the meridian from 10:00 MLT to 22:00 MLT, while in more active situations, it enters the polar cap at prenoon times following the antisunward direction, and then turns to exit around 21:00 MLT. Finally, from these polar cap patterns combined with the auroral statistical models, we build analytical models of the auroral and polar convection expected in steady magnetic conditions.