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Direct imaging has confirmed the existence of substellar companions on wideorbits. To understand the formation and evolution mechanisms of thesecompanions, the full population properties must be characterized. We aim atdetecting giant planet and/or brown dwarf companions around young, nearby, anddusty stars. Our goal is also to provide statistics on the population of giantplanets at wide-orbits and discuss planet formation models. We report a deepsurvey of 59 stars, members of young stellar associations. The observationswere conducted with VLT/NaCo at L'-band (3.8 micron). We used angulardifferential imaging to reach optimal detection performance. A statisticalanalysis of about 60 % of the young and southern A-F stars closer than 65 pcallows us to derive the fraction of giant planets on wide orbits. We usegravitational instability models and planet population synthesis modelsfollowing the core-accretion scenario to discuss the occurrence of thesecompanions. We resolve and characterize new visual binaries and do not detectany new substellar companion. The survey's median detection performance reachescontrasts of 10 mag at 0.5as and 11.5 mag at 1as. We find the occurrence ofplanets to be between 10.8-24.8 % at 68 % confidence level assuming a uniformdistribution of planets in the interval 1-13 Mj and 1-1000 AU. Considering thepredictions of formation models, we set important constraints on the occurrenceof massive planets and brown dwarf companions that would have formed by GI. Weshow that this mechanism favors the formation of rather massive clump (Mclump >30 Mj) at wide (a > 40 AU) orbits which might evolve dynamically and/orfragment. For the population of close-in giant planets that would have formedby CA, our survey marginally explore physical separations (<20 AU) and cannotconstrain this population.

A survey of young, nearby, and dusty stars to understand the formation of wide-orbit giant planets