Distribution system state estimation (DSSE) is one of the key functions used by distribution system operators (DSOs) for the management and control of the distribution grids. In general, distribution networks are featured by a very large number of nodes. Thus, performing the state estimation (SE) of the whole network is computationally demanding. From the system observability point of view, the scarcity of the installed measurement units in the distribution systems is a huge barrier to perform DSSE. Moreover, the unbalanced nature of distribution systems makes estimators based on the positive-sequence model unfit. To tackle these issues, this article presents a new data-driven three-phase state estimator based on an artificial neural network (ANN) and sparse measurements from phasor measurement units (PMUs), together with its observability assessment. Unlike existing estimators performing weakly under non-Gaussian noise, the proposed estimator provides accurate estimates. The proposed SE technique is executed extremely fast (in a few milliseconds). This feature facilitates the real-time monitoring of the distribution grids, as the estimators are coupled with the PMUs. In this context, PMUs play a crucial role as they can provide synchronized phasor measurements with a high reporting rate (f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PMU</sub> > 1 Hz). To reduce the computational cost of the SE problem with distributed computation, multiple ANN three-phase estimators are executed in parallel and integrated in a multiarea SE architecture. The simulation results on the benchmark IEEE 123-bus test system support the feasibility of the solution.