We develop an integrated Multi-Port Concurrent Communication Divisible Load Theory (MPCC-DLT) framework for relay-centric distributed satellite systems (DSS), capturing concurrent data dissemination, parallel computation, and result return under heterogeneous onboard processing and inter-satellite link conditions. We propose a formulation that yields closed-form expressions for optimal load allocation and completion time that explicitly quantify the joint impact of computation speed, link bandwidth, and result-size overhead. We further derive deadline feasibility conditions that enable explicit sizing of cooperative satellite clusters to meet time-critical task requirements. Extensive simulation results demonstrate that highly distributable tasks achieve substantial latency reduction, while communication-heavy tasks exhibit diminishing returns due to result-transfer overheads. To bridge theory and practice, we extend the MPCC-DLT framework with a real-time admission control mechanism that handles stochastic task arrivals and deadline constraints, enabling blocking-aware operation. Our real-time simulations illustrate how task structure and system parameters jointly govern deadline satisfaction and operating regimes. Overall, this work provides the first analytically tractable MPCC-DLT model for distributed satellite systems and offers actionable insights for application-aware scheduling and system-level design of future satellite constellations.