We report on the measurement and computer simulation of the divergence of fast electrons generated in an ultraintense laser-plasma interaction (LPI) and the subsequent propagation in a nonrefluxing target. We show that, at Iλ(2) of 10(20) Wcm(-2)μm(2), the time-integrated electron beam full divergence angle is (60±5)°. However, our time-resolved 2D particle-in-cell simulations show the initial beam divergence to be much smaller (≤30°). Our simulations show the divergence to monotonically increase with time, reaching a final value of (68±7)° after the passage of the laser pulse, consistent with the experimental time-integrated measurements. By revealing the time-dependent nature of the LPI, we find that a substantial fraction of the laser energy (~7%) is transported up to 100 μm with a divergence of 32°.