  We calculate the momentum distribution of the Fermi liquid phase of the
homogeneous, two-dimensional electron gas. We show that, close to the Fermi
surface, the momentum distribution of a finite system with $N$ electrons
approaches its thermodynamic limit slowly, with leading order corrections
scaling as $N^{-1/4}$. These corrections dominate the extrapolation of the
renormalization factor, $Z$, and the single particle effective mass, $m^*$, to
the infinite system size. We show how convergence can be improved analytically.
In the range $1 \le r_s \le 10$, we get a lower renormalization factor $Z$ and
a higher effective mass, $m^*>m$, compared to the perturbative RPA values.
