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In this paper, we study the statistical characterization and modeling of distributed multi-reconfigurable intelligent surface (RIS)-aided wireless systems. Specifically, we consider a practical system model where the RISs with different geometric sizes are distributively deployed, and wireless channels associated to different RISs are assumed to be independent but not identically distributed (i.n.i.d.). We propose two purpose-oriented multi-RIS-aided schemes, namely, the exhaustive RIS-aided (ERA) and opportunistic RIS-aided (ORA) schemes. A mathematical framework, which relies on the method of moments, is proposed to statistically characterize the end-to-end (e2e) channels of these schemes. It is shown that either a Gamma distribution or a Log-Normal distribution can be used to approximate the distribution of the magnitude of the e2e channel coefficients in both schemes. With these findings, we evaluate the …