  Measurements of the midrapidity transverse energy distribution, $d\Et/d\eta$,
are presented for $p$$+$$p$, $d$$+$Au, and Au$+$Au collisions at
$\sqrt{s_{_{NN}}}=200$ GeV and additionally for Au$+$Au collisions at
$\sqrt{s_{_{NN}}}=62.4$ and 130 GeV. The $d\Et/d\eta$ distributions are first
compared with the number of nucleon participants $N_{\rm part}$, number of
binary collisions $N_{\rm coll}$, and number of constituent-quark participants
$N_{qp}$ calculated from a Glauber model based on the nuclear geometry. For
Au$+$Au, $\mean{d\Et/d\eta}/N_{\rm part}$ increases with $N_{\rm part}$, while
$\mean{d\Et/d\eta}/N_{qp}$ is approximately constant for all three energies.
This indicates that the two component ansatz, $dE_{T}/d\eta \propto (1-x)
N_{\rm part}/2 + x N_{\rm coll}$, which has been used to represent $E_T$
distributions, is simply a proxy for $N_{qp}$, and that the $N_{\rm coll}$ term
does not represent a hard-scattering component in $E_T$ distributions. The
$dE_{T}/d\eta$ distributions of Au$+$Au and $d$$+$Au are then calculated from
the measured $p$$+$$p$ $E_T$ distribution using two models that both reproduce
the Au$+$Au data. However, while the number-of-constituent-quark-participant
model agrees well with the $d$$+$Au data, the additive-quark model does not.
