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We present our magnetooptical Kerr effect (MOKE) studies on picosecond spin dynamics in closely spaced rectangular Co dots with sizes ranging from 2×6 μm2 down to 100 × 300 nm2 under in-plane, picosecond, magnetic pulse excitation. A low-temperature-grown GaAs photoconductive switch, excited by femtosecond laser pulses, was used to produce ∼25-ps-long magnetic transients along the surface of the coplanar-waveguide centerline, which contained arrays of patterned Co dots. The resulting spin dynamics in the dots was detected by a time-synchronized train of femtosecond optical probe pulses employing the time-resolved MOKE. Our experimental technique allowed us to measure the initial picosecond dynamics of spins in Co nanodots, followed by damped oscillations. We ascribe the observed results to the small-angle coherent spin precession and show that it depends on the size of magnetic dots.