In this work, we propose Aplasia, an holistic architecture with a radical design. Aiming at simplifying the inner network devices (and so their cost), we tradeoff node architecture- and algorithmic-complexity for an increased (but tunable) communication cost. The main ingredients of our recipe are (i) the use of complete paths directly in the frames header, that allows core devices to perform data-plane switching functions without lookup and (ii) the use of a greedy probabilistic routing algorithm to quickly discover multiple, near optimal, paths in the control plane. We extensively simulate, analyze and implement our proposal to testify its soundness.