Accurate knowledge of the morphology of halos and its evolution are key constraints on the galaxy formation model as well as a determinant parameter of the strong-lensing phenomenon. Using the cosmological hydrodynamic simulation, the Evolution and Assembly of GaLaxies and their Environments (EAGLE), we aim to provide a comprehensive analysis of the evolution of the morphology of galaxy halos and of their mass distributions with a focus on the snapshot at redshift $z=0.5$. We developed an iterative strategy involving a principal component analysis (PCA) to investigate the properties of the EAGLE halos and the differences in alignment between the various components. The mass distributions of the dark-matter (DM), gas, and star halos are characterised by a half-mass radius, a concentration parameter and (projected) axis ratios. We present statistics of the shape parameters of 336 540 halos from the EAGLE RefL0025N0376 simulation and describe their evolution from redshift $z=15$ to $z=0$. We measured the three-dimensional and two-dimensional projected shape parameters for the DM, the gas, and the star components as well as for all particles. At $z=0.5$, the minor axis of gas aligns with the minor axis of DM for massive halos ($M>10^{12}$ M$_\odot$), but this alignment is poorer for less massive halos. The DM halos axis ratios $b/a$ and $c/a$ have median values of $0.82 \pm 0.11$ and $0.64 \pm 0.12$, respectively. The sphericity of gas in halos w/ and w/o stars appears to be negatively correlated to the total mass, while the sphericity of DM is insensitive to it. The measured projected axis ratios, $b_p/a_p$, of star halos at $z=0.5$ have a median value of $0.80 \pm 0.07$, which is in good agreement with ground-based and space-based measurements within 1 $\sigma$. For DM halos, we measure a value of $0.85 \pm 0.06$.< Leer menos