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The complex radio-propagation environment inside buildings often necessitates site-specific radio planning/modeling/measurements in designing an in-building wireless network. With the emergence of very-low-cost distributed-antenna hardware, it becomes economically feasible to blanket a building with a large number of antenna elements (the "saturating approach"). We investigate the characteristic radio distribution statistics (for both radio-power and delay-spread) under this scenario, and found that with a "sufficiently large" number of antenna elements per unit area, these radio statistics approach certain universal distributions which are largely independent of the specific floor-plan, and which can be accurately predicted, without invoking adjustable parameters, using only a few easily-determinable "global" building parameters. Comparison with experimental measurements yields excellent agreements.