The incorporation of oxygen into YBa2Cu3O6+x (YBaCuO) thin films during in situ growth by pulsed laser deposition (PLD) has been investigated as a function of the ablation conditions. A quenching technique has been used immediately after termination of growth to avoid any oxygen in or out-diffusion during the cooling down step. It is shown that superconducting YBaCuO thin films can be formed without any post-oxygenation procedure, contrary to what is expected from the (Image, T) thermodynamic diagram. Moreover, it is found that there is an optimal target-substrate distance, D, for each O2 deposition pressure, Image, that leads to the higher critical temperature (i.e., higher oxygenation) as well as to the best structural and morphological properties of quenched films. The results are discussed considering the formation of reactive oxygen in the laser-induced plasma during film growth.