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A detailed statistical study of the magnetic structure of the dayside polar cusps is presented, based on multi-year sets of magnetometer data of Polar and Cluster spacecraft, taken in 1996–2006 and 2001–2007, respectively. Thanks to the dense data coverage in both Northern and Southern Hemispheres, the analysis spanned nearly the entire length of the cusps, from low altitudes to the cusp "throat" and the magnetosheath. Subsets of data falling inside the polar cusp "funnels" were selected with the help of TS05 and IGRF magnetic field models, taking into account the dipole tilt and the solar wind/IMF conditions. The selection funnels were shifted within ±10° of SM latitude around the model cusp location, and linear regression parameters were calculated for each sliding subset, further divided into 10 bins of distance in the range 2≤<I>R</I>≤12 <I>R<sub>E</sub></I>, with the following results. (1) Diamagnetic depression, caused by the penetrated magnetosheath plasma, becomes first visible at <I>R</I>~4–5 <I>R<sub>E</sub></I>, rapidly deepens with growing <I>R</I>, peaks at <I>R</I>~6–9 <I>R<sub>E</sub></I>, and then partially subsides and widens in latitude at the cusp's outer end. (2) The depression peak is systematically shifted poleward (by ~2° of the footpoint latitude) with respect to the model cusp field line, passing through the min{|<I><B>B</B></I>|} point at the magnetopause. (3) At all radial distances, clear and distinct peaks of the correlation between the local <I>B<sub>y</sub></I> and <I>B<sub>y</sub></I><sup>(IMF)</sup> and of the corresponding proportionality coefficient are observed. A remarkably regular variation of that coefficient with <I>R</I> quantitatively confirms the field-aligned geometry of the cusp currents associated with the IMF <I>B<sub>y</sub></I>, found in earlier observations.