Distinct from conventional Eulerian 2D fluid solvers, applied routinely to magnetic fusion edge plasma studies, complex 3D magnetic topologies are currently treated by the geometrically more flexible Lagrangian schemes, supplemented by Monte Carlo procedures for higher order derivatives (dissipative terms due to diffusion processes) and sources. These particle based algorithms are combined with a field line reconstruction technique for dealing with partially ergodic magnetic fields, involving field aligned regular grids. A generalization to block-structured grids is carried out, which greatly enhances the applicability range of present 3D fusion plasma edge codes, in particular also to poloidally magnetic diverted configurations, as currently envisaged for the largest magnetic fusion device under construction: ITER.