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We have studied the magnetic and power absorption properties of a series of magnetic nanoparticles (MNPs) of Fe3O4 with average sizes langdrang ranging from 3 to 26 nm. Heating experiments as a function of particle size revealed a strong increase in the specific power absorption (SPA) values for particles with langdrang = 25-30 nm. On the other side saturation magnetization MS values of these MNPs remain essentially constant for particles with langdrang above 10 nm, suggesting that the absorption mechanism is not determined by MS. The largest SPA value obtained was 130 W/g, corresponding to a bimodal particle distribution with average size values of 17 and 26 nm.