The problems of diffusive transport to and across an irregular interface are of general interest, but are considered a difficult class of problems for theoretical understanding. In this paper we discuss theory of partial diffusion-limited interfacial transfer/reaction on a realistic fractal interface. The surface irregularity is modeled as a random surface fractal, which is characterized by statistically isotropic self-affine fractals on limited length scales. The power spectrum of roughness of such surface fractal is approximated in terms of power law function for the intermediate wave-numbers (or spatial frequency components in roughness). This description of roughness consists of four fractal morphological characteristic features. Results unravel the connection between the flux/current, surface morphology and its kinetics following a step of surface activity (like a potential step experiment). We show the dependence of reaction flux/current on various fractal roughness characteristics related to power spectrum, and discuss the dynamic crossover of charge transfer controlled regime to fractal morphology controlled diffusion regime to classical inverse square root of time regime. (C) 2009 Elsevier B.V. All rights reserved.