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Writing with ink on a paper and the rapid diagnostics of diseases using paper cartridge, despite their remarkable diversities from application perspective, both involve the motion of a liquid from a source on a porous hydrophilic substrate. Here we bring out a generalization in the pertinent dynamics by appealing to the concerned ensemble-averaged transport with reference to the underlying molecular picture. Our results reveal that notwithstanding the associated complexities and diversities, the resultant liquid transport characteristics on a paper matrix, in a wide variety of applications, resemble universal diffusive dynamics. Agreement with experimental results from diversified applications is generic and validates our unified theory. [ABSTRACT FROM AUTHOR]