Structural and magnetic properties of Co50 ± x Pt50± x films 25-50 nm thick, prepared by molecular beam epitaxy onto a Pt buffer grown on MgO (001) substrate have been investigated. A series of 3 samples with different compositions (x = 6, 0, -6) was grown at 800 K on a 10 nm thick Pt buffer and another series of 5 samples of equiatomic composition was prepared at various growth temperatures (390 K≤ TG≤ 780 K) on a Pt buffer 4 nm thick. X-ray diffraction and TEM studies show the presence of grains with  and  orientations, the  grains being a mixture of the tetragonal L10 ordered phase and of the fcc disordered one. Both the thickness of the buffer layer and the deposition temperature are determinant parameters of the structural quality of the films and of the degree of long range order (LRO). An apparent LRO parameter (ηapp) is deduced from the superstructure and main peak intensity ratio. Its increase with the growth temperature is described through a thermally activated model that yields a small activation energy of 0.28 eV, illustrating the role played by both surface diffusion and surface interactions in building the L10 compound in agreement with theoretical predictions. An average uniaxial magnetocrystalline anisotropy energy (Ku av) is deduced from the magnetization curves measured by a SQUID. The anisotropy energy of the  grains (Ku 002) is deduced, assuming a linear relationship between the anisotropies and the phase percentages. One observes a continuous but not linear increase of Ku 002 with ηapp.