The response of lean (ϕ 6 0.4) premixed hydrogen flames to maintained homogeneous isotropic turbulence is investigated using detailed numerical simulation in an idealised three-dimensional configuration over a range of Karlovitz numbers from 10 to 1562. In particular, a focus is placed on turbulence sufficiently intense that the flames can no longer be considered to be in the thin reaction burning regime. This transition to the so-called distributed burning regime is characterised through a number of diagnostics, and the relative roles of molecular and turbulent mixing processes are examined. The phenomenology and statistics of these flames are contrasted with a distributed thermonuclear flame from a related astrophysical study.