Transport properties through wide and short ballistic graphene junctions are studied in the presence of arbitrary dopings and magnetic fields. No dependence on the magnetic field is observed at the Dirac point for any current cumulant, just as in a classical diffusive system, both in normal-graphene-normal and normalgraphene- superconductor junctions. This pseudodiffusive regime is, however, extremely fragile with respect to doping at finite fields. We identify the crossovers to a field-suppressed and a normal ballistic transport regime in the magnetic-field-doping parameter space, and provide a physical interpretation of the phase diagram. Remarkably, pseudodiffusive transport is recovered away from the Dirac point in resonance with Landau levels at high magnetic fields.