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We report the thickness dependence of the Dzyaloshinskii-Moriya interaction (DMI) and spin-orbit torques (SOTs) in Pt\Co(t)\AlOx, studied by current-induced domain wall (DW) motion and second-harmonic experiments. From the DW motion study, a monotonous decay of the effective DMI strength with increasing Co thickness is observed, in agreement with a DMI originating from the Pt\Co interface. The study of the ferromagnetic layer thickness dependence of spin-orbit torques reveals a more complex behavior. The observed thickness dependence suggests the spin-Hall effect in Pt as the main origin of the SOTs, with the measured SOT-fields amplitudes resulting from the interplay between the varying thickness and the transverse spin diffusion length in the Co layer.