We study the growth and relaxation processes of Ge crystals selectively grown by chemical vapour deposition on free-standing 90 nm wide Si(001) nanopillars. Epi-Ge with thickness ranging from 4 to 80 nm was characterized by synchrotron based x-ray diffraction and transmission electron microscopy. We found that the strain in Ge nanostructures is plastically released by nucleation of misfit dislocations, leading to degrees of relaxation ranging from 50 to 100%. The growth of Ge nanocrystals follows the equilibrium crystal shape terminated by low surface energy (001) and {113} facets. Although the volumes of Ge nanocrystals are homogeneous, their shape is not uniform and the crystal quality is limited by volume defects on {111} planes. This is not the case for the Ge/Si nanostructures subjected to thermal treatment. Here, improved structure quality together with high levels of uniformity of the size and shape is observed.