  We present a microscopic model for nanoparticles, of the maghemite ($\gamma
$% -Fe$_{2}$O$_{3}$) type, and perform classical Monte Carlo simulations of
their magnetic properties. On account of M\"{o}ssbauer spectroscopy and
high-field magnetisation results, we consider a particle as composed of a core
and a surface shell of constant thickness. The magnetic state in the particle
is described by the anisotropic classical Dirac-Heisenberg model including
exchange and dipolar interactions and bulk and surface anisotropy. We consider
the case of ellipsoidal (or spherical) particles with free boundaries at the
surface. Using a surface shell of constant thickness ($\sim 0.35$ nm) we vary
the particle size and study the effect of surface magnetic disorder on the
thermal and spatial behaviors of the net magnetisation of the particle. We
study the shift in the surface ``critical region'' for different
surface-to-core ratios of the exchange coupling constants. It is also shown
that the profile of the local magnetisation exhibits strong temperature
dependence, and that surface anisotropy is reponsible for the non saturation of
the magnetisation at low temperatures.
