  We study the interplay between the effects of surface anisotropy and dipolar
interactions in monodisperse assemblies of nanomagnets with oriented
anisotropy. We derive asymptotic formulas for the assembly magnetization taking
account of temperature, applied field, core and surface anisotropy, and dipolar
inter-particle interactions. We find that the interplay between surface
anisotropy and dipolar interactions is well described by the analytical
expression of the assembly magnetization derived here: the overall sign of the
product of the two parameters governing the surface and the dipolar
contributions determines whether intrinsic and collective terms compete or have
synergistic effects on the magnetization. This is illustrated by the
magnetization curves of $\gamma-Fe_{2}O_{3}$ nanoparticles assemblies in the
low concentration limit.
