Epitaxial growth of a submonolayer amount of C, followed by 2-4 monolayers (ML) Ge results in the formation of extremely small C-induced Ge (CGe) quantum dots. Different stacks of CGe islands combined with pure Ge island layers are fabricated. We present vertical coherent quantum dot stacks, consisting of an initial 0.2 ML C/3 ML Ge dot layer, followed by five layers of 4 ML Ge. Each layer is separated by 1 nm of Si. The islanding process is initiated before the critical thickness for planar Ge growth is reached and results in only 20 nm wide and 2 nm high vertically aligned Ge dots. However, if we substitute the pure Ge layers by CGe dot layers, no vertical correlation is observed. We explain this phenomenon by the: kinetically limited process of CGe island formation. itself.