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We examine height-height correlations in the transient growth regime of the2+1 Kardar-Parisi-Zhang (KPZ) universality class, with a particular focus onthe {\it spatial covariance} of the underlying two-point statistics,higher-dimensional analog of the 1+1 KPZ Class Airy$_1$ process. Makingcomparison to AFM kinetic roughening data in 2d organic thin films, we use ouruniversal 2+1 KPZ spatial covariance to extract key scaling parameters for thisexperimental system. Additionally, we explore the i) height, ii) localroughness, and iii) extreme value distributions characteristic of theseoligomer films, finding compelling agreement in all instances with ournumerical integration of the KPZ equation itself. Finally, investigatingnonequilibrium relaxation phenomena exhibited by 2+1 KPZ Class models, we haveunearthed a universal KPZ ageing kinetics. In experiments with ample data inthe time domain, our 2+1 KPZ Euler {\it temporal covariance} will allow aquick, independent estimate of the central KPZ scaling parameter.

Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth