We propose a method of derivation of global asymptotic solutions of the hydromagnetic dynamo problem at large magnetic Reynolds number. The procedure reduces to matching the local asymptotic forms for the magnetic field generated near individual extrema of generation strength. The basis of the proposed method, named here theMaximally-Efficient-GenerationApproach (MEGA), is the assertion that properties of global asymptotic solutions of the kinematic dynamo are determined by the distribution of the generation strength near its leading extrema and by the number and distribution of the extrema.