Reflexion high-energy electron diffraction (RHEED), transmission electron microscopy (TEM) along with physical property measurement system (PPMS) were used to investigate the growth kinetics of Ge1-xMnx diluted magnetic semiconductors (DMS) grown on Ge(001) by means of molecular beam epitaxy (MBE). At a given intermediate growth temperature of 130 degrees C, we have identified the formation of successive heterogeneous phases when increasing the Mn concentration from 1 to 14 %: DMS phase containing nanosized Mn-rich clusters for x below 2%, DMS phase containing high Curie temperature (T-C) nanocolumns for x ranging from 5 to 6 %, DMS phase in which GeMn nanocolumns and Mn5Ge3 clusters coexist and then finally DMS containing mainly Mn5Ge3 clusters at Mn concentration higher than 12%. Our results confirm that the low solubility of Mn in Ge is the main origin of the formation of heterogeneous phases and provide evidence that it is extremely difficult to form a homogenous GeMn DMS even for Mn concentrations being below 2%. We also demonstrate that high-TC nanocolumns and Mn5Ge3 clusters are competing processes and the process window corresponding to the stabilisation of high-T-C nanocolumns remains extremely tight.