Optimal power allocation, in a wireless sensor network with a fusion center, for distributed parameter estimation under a total network power constraint is considered. For the simple star topology, an analysis of the effect of the measurement noise variance on the optimal power allocation policy is presented. As the measurement noise variance increases, the optimal solution evolves from sensor selection to power equalization - the sensor with the lowest SNR is allocated the largest fraction of the total power.Relaying nodes are introduced to form more complicated branch, tree and linear topologies. The optimal power allocation strategies for these topologies are then considered for both amplify-and-forward and estimate-and-forward transmission protocols. Analytical solutions for these cases are intractable, and thus asymptotically (for increasing measurement noise variance) optimal solutions are derived.