We have measured the critical phase change conditions induced by electrical pulses in Ge2Sb2Te5 nanopillar phase change memory devices by constructing a comprehensive resistance map as a function of pulse parameters (width, amplitude and trailing edge). Our measurements reveal that the heating scheme and the details of the contact geometry play the dominant role in determining the final phase composition of the device such that a non-uniform heating scheme promotes partial amorphization/crystallization for a wide range of pulse parameters enabling multiple resistance levels for data storage applications. Furthermore we find that fluctuations in the snap-back voltage and set/reset resistances in repeated switching experiments are related to the details of the current distribution such that a uniform current injection geometry (i.e. circular contact) favors more reproducible switching parameters. This shows that possible geometrical defects in nanoscale phase change memory devices may play an essential role in the performance of the smallest possible devices through modification of the exact current distribution in the active chalcogenide layer. We present a three-dimensional finite element model of the electro-thermal physics to provide insights into the underlying physical mechanisms of the switching dynamics as well as to quantitatively account for the scaling behaviour of the switching currents in both circular and rectangular contact geometries. The calculated temporal evolution of the heat distribution within the pulse duration shows distinct features in rectangular contacts providing evidence for locally hot spots at the sharp corners of the current injection site due to current crowding effects leading to the observed behaviour.