In organic light emitting diodes with small area the current may be dominated by a finite number, N of sites in which the electron-hole recombination occurs. As a result, averaging over the hyperfine magnetic fields, b_h, that are generated in these sites by the environment nuclei is incomplete. This creates a random (mesoscopic) current component, {Delta}I(B), at field B having relative magnitude ~ N^(-1/2). To quantify the statistical properties of {Delta}I(B) we calculate the correlator K(B, {Delta}B)= <{delta}I(B - {Delta}B/2){delta}I(B + {Delta}B/2)> for parallel and perpendicular orientations of {Delta}B. We demonstrate that mesoscopic fluctuations develop at fields B>>b_h, where the average magnetoresistance is near saturation. These fluctuations originate from the slow beating between S and T_0 states of the recombining e-h spin pair-partners. We identify the most relevant processes responsible for the current fluctuations as due to anomalously slow beatings that develop in sparse e-h polaron pairs at sites for which the b_h projections on the external field direction almost coincide.
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