Using numerical simulation, recent research on the properties of unit root tests in the presence of generalised autoregressive conditional heteroskedasticity (GARCH) is extended. The principal development concerns consideration of relative properties of linear and non–linear unit root tests in the presence of heavy–tailed GARCH innovations via the use of the student–t distribution and the generalised error distribution. The results obtained show the non–linear unit root test of Kapetanios et al. (2003) to suffer far greater finite–sample size distortion than the linear Dickey–Fuller test. The impact of heteroskedasticity consistent covariance matrix estimators is also considered. It is found that these 'robust' methods are unable to guarantee size correction in the presence of heavy–tailed GARCH processes and have differing effects depending upon the exact estimator used and whether they are applied to linear or non–linear unit root tests.