— This paper investigates theoretical aspects of the uneven energy depletion phenomenon recently noticed in sink-based wireless sensor networks. We consider uniformly distributed sensors, each sending roughly the same number of reports toward the closest sink. We assume an energy consumption model governed by the relation E = dα +c where d, (d ≤ tx), is the transmission distance, α ≥ 2 is the power attenuation, c is a technology-dependent positive constant, and tx is the maximum transmission range of sensors. Our results are multifold. First, we show that for α > 2, all sensors whose distance to the sink is min{tx, ( 2c α−2 ) 1 α } should transmit directly to the sink. Interestingly, this limit does not depend on the size of the network, expressed as the largest distance R from a sensor to the closest sink. Next, we prove that in order to minimize the total amount of energy spent on routing along a path originating at a sensor in a corona and ending at the sink, all the...