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We aim at characterizing the accretion properties of several hundred members of the star-forming cluster NGC 2264 (3 Myr). We performed a deep u,g,r,i mapping and a simultaneous u+r monitoring of the region with CFHT/MegaCam in order to directly prob e the accretion process from UV excess measurements. Photometric properties and stellar parameters are determined homogeneously for about 750 monitored young objects, spanning the mass range 0.1-2 Mo. About 40% are classical (accreting) T Tauri stars, based on various diagnostics (H_alpha, UV and IR excesses). The remaining non-accreting members define the (photospheric+chromospheric) reference UV emission level over which flux excess is detected and measured. We revise the membership status of cluster members based on UV accretion signatures and report a new population of 50 CTTS candidates. A large range of UV excess is measured for the CTTS population, varying from a few 0.1 to 3 mag. We convert these values to accretion luminosities and obtain mass accretion rates ranging from 1e-10 to 1e-7 Mo/yr. Taking into account a mass-dependent detection threshold for weakly accreting objects, we find a >6sigma correlation between mass accretion rate and stellar mass. A power-law fit, properly accounting for upper limits, yields M_acc $propto$ M^{1.4+/-0.3}. At any given stellar mass, we find a large spread of accretion rates, extending over about 2 orders of magnitude. The monitoring of the UV excess on a timescale of a couple of weeks indicates that its variability typically amounts to 0.5 dex, much smaller than the observed spread. We suggest that a non-negligible age spread across the cluster may effectively contribute to the observed spread in accretion rates at a given mass. In addition, different accretion mechanisms (like, e.g., short-lived accretion bursts vs. more stable funnel-flow accretion) may be associated to different M_acc regimes.
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