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For a general energy harvesting (EH) communication network, i.e., a network where the nodes generate their transmit power through EH, we derive the asymptotically optimal online power allocation solution that optimizes a general utility function when the number of transmit time slots, N, and the battery capacities of the EH nodes, B _max , satisfy N → ∞ and B _max → ∞. The considered family of utility functions is general enough to include the most important performance measures in communication theory, such as the average data rate, outage probability, average bit-error probability, and average signal-to-noise ratio. The proposed power allocation solution is very simple. Namely, the asymptotically optimal power allocation for the EH network is identical to the optimal power allocation for an equivalent nonEH network whose nodes have infinite energy available but their average transmit power is constrained to …