of the observable DCO populations which incorporates cosmological evolution and accurate models of the gravitational waveforms is particularly timely. This is the goal of this paper, the third in a series [cf. @dominik; @dominik2]. Our work builds on the results presented in the second paper [@dominik2 henceforth Paper 2], where we presented the cosmological distribution of DCOs for a set of four evolutionary models. These models investigated a range of Hertzsprung gap (HG) common envelope (CE) donors, supernova (SN) explosion engines, and BH natal kicks, showing distinct differences in the properties of the resulting DCO populations. Population models were placed in a cosmological context by adopting the star formation history reported in [@strolger] and the galaxy mass distribution of [@fontana], both of which are redshift-dependent. We performed all calculations assuming two scenarios for metallicity evolution, meant to bracket the uncertainties associated with the chemical composition of the Universe. Binary evolution was performed using the [StarTrack]{} population synthesis code [@startrack]. In this work we complete and extend the analysis of Paper 2. We study the detection rates and the expected physical properties of coalescing DCOs at cosmological distances for second-generation GW observatories. The rates are calculated for different sets of gravitational 