Broadband dielectric spectroscopy is used to investigate molecular dynamics and charge transport in three hyper-branched polyester amides with hydroxyl, phenyl, and stearate terminal groups. At higher temperatures, the dielectric spectra are interpreted in terms of hopping conduction in a spatially randomly varying energy landscape, whereas two secondary dipolar relaxations attributed to librations of the terminal and amide groups dominate the low temperature regime. Despite a shift of more than 3 decades in the dc conductivity upon variation of the end groups, the Barton-Nakajima-Namikawa relation is shown to hold. (C) 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1651-1657, 2010