[en] The statistical mechanics of submonolayer helium films on graphite substrates are conventionally described by site localization models. However, dynamical experiments indicate high mobility so that a solid state band picture might be more appropriate. As a theoretical test case, the authors consider dilute two dimensional hard core quantum fluids and find logarithmic divergences not present in the well known three dimensional counterparts. These divergences are not a serious obstacle to band theoretical models which include interactions. (Auth.)