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The physics of the "hot spots" on stellar surfaces and the associated variability of accreting magnetized rotating stars is investigated for the first time using fully three-dimensional magnetohydrodynamic simulations. The magnetic moment of the star is inclined relative to its rotation axis by an angle Theta. A sequence of misalignment angles was investigated, between Theta=0 and 90 degrees.Typically at small Theta the spots are observed to have the shape of a bow which is curved around the magnetic axis, while at largest Theta the spots have a shape of a bar, crossing the magnetic pole. The physical parameters (density, temperature, etc.) increase toward the central regions of the spots. At relatively low density and temperature, the spots occupy approximately 10-20 % of the stellar surface, while at the highest values of these parameters this area may be less than 1 % of the area of the star. The light curves were calculated for different Theta and inclination angles of the disk i. They show a range of variability patterns, including one maximum-per-period curves (at most of angles Theta and i), and two maximum-per-period curves (at large Theta and i). At small Theta, the funnel streams may rotate faster/slower than the star, and this may lead to quasi-periodic variability of the star. The results are of interest for understanding the variability and quasi-variability of Classical T Tauri Stars, millisecond pulsars and cataclysmic variables.