The magnetic and transport properties of films based on discontinuous layers of Ni81Fe19 (Py) embedded inAl2O3 were investigated. In films with nominal Py thicknesses 6 and 8 Å superparamagnetic particles withmedian diameters Dmed=2.8 and 3.1 nm and distribution widths s_D=1.2 and 1.3 nm were formed. Current-voltage (IU) curves were measured with the current perpendicular to the film plane. The analyses show that thecharge transport occurs via tunneling; with the charging energy supplied by thermal fluctuations at hightemperature, T>100 K, and by the electric field at low temperature, T<10 K. The separation of the tworegimes allows independent estimates of the mean charging energy <EC>~40 meV for both samples; from theresistance R versus T analyzed in an effective-medium model at high temperature and from I versus U at 4 K.In order to obtain a consistent description of the transport properties, the size distributions must be included toaccount for the deviation from the single size behavior R~exp(EC/kBT) at high T. The scaling parameter inthe relation I \propto (U/Uth−1)^g, where Uth is the threshold for conduction, is estimated to g~2 at 4 K. The superparamagneticrelaxation of the particles becomes blocked below a temperature T~20 K respective 30 K for 6and 8 Å. The magnetic field (B) dependence of the resistance R(B) displays a single maximum of the ratio MR=[R(B)−R(2 T)] /R(2 T) in zero field at room temperature and a characteristic splitting of the peak at 4K, attributed to the blocking. The maxima, ~0.9% for 6 Å and 1.1% for 8 Å, are positioned at fields abouta factor of two to three higher than the coercive fields of the samples