  In a two-dimensional parabolic quantum dot charged with $N$ electrons,
Thomas-Fermi theory states that the ground-state energy satisfies the following
non-trivial relation: $E_{gs}/(\hbar\omega)\approx N^{3/2}
f_{gs}(N^{1/4}\beta)$, where the coupling constant, $\beta$, is the ratio
between Coulomb and oscillator ($\hbar\omega$) characteristic energies, and
$f_{gs}$ is a universal function. We perform extensive Configuration
Interaction calculations in order to verify that the exact energies of
relatively large quantum dots approximately satisfy the above relation. In
addition, we show that the number of energy levels for intraband and interband
(excitonic and biexcitonic) excitations of the dot follows a simple exponential
dependence on the excitation energy, whose exponent, $1/\Theta$, satisfies also
an approximate scaling relation {\it a la} Thomas-Fermi,
$\Theta/(\hbar\omega)\approx N^{-\gamma} g(N^{1/4}\beta)$. We provide an
analytic expression for $f_{gs}$, based on two-point Pad\'e approximants, and
two-parameter fits for the $g$ functions.
