The transport of relativistic electrons1 generated in wire and foil targets by short-pulse lasers is examined with the new e-PLAS simulation code based on implicit-moment/hybrid2 techniques. In a 50 μm diameter Cu wire (Zeff = 15) as recently illuminated on the TITAN LLNL laser, for example, a 1.7×1020 W/cm2 simulated laser beam delivering a flat 30 μm spot from the left (with 40 % absorption) generates the hot electron density profile depicted below at 940 fs. The peak hot density in the laser spot is ∼3×1021 electrons/cm3. This density drops to 3x1019 electrons/cm3 200 microns into the wire. A peak temperature of 2 keV is achieved through Joule heating of the background electrons in the wire “head” near the deposition surface; a significantly lower ∼0.4 keV is achieved in the wire body. Here, 300 MG thermoelectric B-fields are also calculated. Parameter studies relate the hot electron stopping to the surface B-field, modest drag slowing, and the background cold electron resisitvity, which is bleached by background heating to low values at late times.