RESUMEN

Every branched superminimal suface of area 4πd I S⁴ is shown to arise from a pair of meromorphic functions (f₁,f₂) of bidegree (d,d) such that f₁ and f₂ have the same ramification divisor. Conditions under which branched superminimal surfaces can be generated from such pairs of functions are derived. For each d ≥1 the space of harmonic maps (i.e branched superminimal immersions) of S² into S⁴ of harmonic degree d is shown to be a connected space of complex dimension 2d + 4.