Over the past decade, a growing number of deep imaging surveys have started to provide meaningful constraints on the population of extrasolar giant planets at large orbital separation. Primary targets for these surveys have been carefully selected based on their age, distance and spectral type, and often on their membership to young nearby associations where all stars share common kinematics, photometric and spectroscopic properties. The next step is a wider statistical analysis of the frequency and properties of low mass companions as a function of stellar mass and orbital separation. In late 2009, we initiated a coordinated European Large Program using angular differential imaging in the H band (1.66 μm) with NaCo at the VLT. Our aim is to provide a comprehensive and statistically significant study of the occurrence of extrasolar giant planets and brown dwarfs at large (5-500 AU) orbital separation around ~150 young, nearby stars, a large fraction of which have never been observed at very deep contrast. The survey has now been completed and we present the data analysis and detection limits for the observed sample, for which we reach the planetary-mass domain at separations of ≳50 AU on average. We also present the results of the statistical analysis that has been performed over the 75 targets newly observed at high-contrast. We discuss the details of the statistical analysis and the physical constraints that our survey provides for the frequency and formation scenario of planetary mass companions at large separation.