This paper investigates the performance of scalable user-centric (UC) distributed massive multiple-input multiple- output (D-mMIMO) systems, widely known in the literature as cell-free mMIMO, with limited processing capacity. Specifically, it is assumed that the computational complexity (CC) of performing channel estimation and precoding signals does not increase with the number of access points (APs). In this regard, it is considered that each user equipment (UE) can only be associated with a finite number of APs. Moreover, a method is proposed for adjusting the AP clusters according to the network implementation, i.e., centralized or distributed. We compare the proposed approaches with a scalable UC system that does not perform AP cluster adjustment and does not prevent the processing demands from growing with the number of APs. Simulation results reveal that UC systems can keep the spectral efficiency (SE) under minor degradation even if the processing capacity is limited, reducing the CC by up to 96%. Besides, the proposed method for adjusting the AP cluster leads to further reductions in CC.