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Measurements of the midrapidity transverse energy distribution, dET /dη, are presented for p+p, d+Au, and Au+Au collisions at √ s N N = 200 GeV and additionally for Au+Au collisions at √ s N N = 62.4 and 130 GeV. The dET /dη distributions are first compared with the number of nucleon participants Npart, number of binary collisions N coll , and number of constituent-quark participants Nqp calculated from a Glauber model based on the nuclear geometry. For Au+Au, dET /dη /Npart increases with Npart, while dET /dη /Nqp is approximately constant for all three energies. This indicates that the two component ansatz, dET /dη ∝ (1 − x)Npart/2 + xN coll , which has been used to represent ET distributions, is simply a proxy for Nqp, and that the N coll term does not represent a hard-scattering component in ET distributions. The dET /dη distributions of Au+Au and d+Au are then calculated from the measured p+p ET 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.