Supported by experiment, we establish the following for the current flow across the epitaxial collector layer of a bipolar transistor biased at the onset of base-widening effects. The flow is one-dimensional only for large collector-base voltages, when it is space-charge limited and velocity saturated. As the collector-base voltage is lowered and the device enters quasi-saturation, the flow spreads progressively. The variation of the collector current with collector-base voltage, taking into account current spreading effects, is well modeled by a simple saturating exponential function with physically based constants. (C) 2003 Elsevier Science Ltd. All rights reserved.