The transport of electrons in semiconductor heterolayers under the influence of high crossed electric and magnetic fields has been investigated. Particular attention has been paid to real-space transfer effects. For the first time it is shown in a direct fashion that real-space transfer is associated with a transition of the two-dimensional electron gas to a three-dimensional electron distribution. This transition manifests itself by the sudden appearance of magnetoresistance (positive or negative) in perpendicular electric and magnetic fields at a critical electric field strength. Experimental results for various strengths and orientations of the magnetic field are presented and compared with a Monte Carlo transport simulation which included the Lorentz force.