In this paper, the performance of orthogonal space-time block codes (OSTBC) for distributed multiple-input multiple-output (MIMO) systems employing adaptive M-QAM transmission is investigated over independent but not necessarily identically distributed (i.n.i.d.) generalized-K fading channels with arbitrary positive integer-valued k(inversely reflects the shadowing severity) and m (inversely reflects the fading severity). Before this, i.n.i.d. generalized-K fading channel has never been considered for distributed OSTBC-MIMO systems. Especially, the effects of the shape parameter k on the distributed OSTBC-MIMO system performance are unknown. Thus, we investigate mainly the significance of the shape parameter k on the distributed OSTBC-MIMO system performance, in terms of the average symbol error probability (SEP), outage probability, and spectral efficiency (SE). By establishing the system model, the approximated probability density function (PDF) of the equivalent signal to noise ratio (SNR) is derived and thereafter the approximated closed-form expressions of the above performance metrics are obtained successively. Finally, the derived expressions are validated via a set of Monte-Carlo simulations and the implications of the shape parameter k on the overall performance are highlighted.