Are there so many sons per node in a wireless sensor network data aggregation tree?

Some authors seem to believe that the average number of sons in a Wireless Sensor Network (WSN) data aggregation tree can be kept constant, even when the distances from the sink increase. But this assumption is impossible to stand in a dense and uniformly deployed network, as the number of nodes in a given level would grow exponentially, while the perimeter just grows linearly. In this letter, it is shown that the average number of sons of a given tree node is in average a quite low number, slightly higher than one, and that it tends to 1, as the distance to sink, or node depth, increases, both for 2-D, and for 3-D WSNs.