We develop robust targeted maximum likelihood estimators (TMLEs) for transporting intervention effects from one population to another. Specifically, we develop TMLEs for three transported estimands: the ¡ntent-to-treat average treatment effect (ATE) and complier ATE, which are relevant for encouragement design interventions and instrumental variable analyses, and the ATE of the exposure on the outcome, which is applicable to any randomized or observational study. We demonstrate finite sample performance of these TMLEs by using simulation, including in the presence of practical violations of the positivity assumption. We then apply these methods to the 'Moving to opportunity' trial: a multisite, encouragement design intervention in which families in public housing were randomized to receive housing vouchers and logistical support to move to low poverty neighbourhoods. This application sheds light on whether effect differences across sites can be explained by differences in population composition.