  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.
