  We present HI-based B- and R-band Tully-Fisher relations (TFRs) and the
Baryonic TFR (BTFR) at z=0.2 using direct HI detections from the Blind
Ultra-Deep HI Environmental Survey (BUDHIES). Deep photometry from the Isaac
Newton Telescope was used for 36 out of 166 HI sources, matching the quality
criteria required for a robust TFR analysis. Two velocity definitions at 20%
and 50% of the peak flux were measured from the global HI profiles and adopted
as proxies for the circular velocities. We compare our results with an
identically constructed z=0 TFR from the Ursa Major (UMa) association of
galaxies. To ensure an unbiased comparison of the TFR, all the samples were
treated identically regarding sample selection and applied corrections. We
provide catalogues and an atlas showcasing the properties of the galaxies. Our
analysis is focused on the zero points of the TFR and BTFR with their slopes
fixed to the z=0 relation. Our main results are: (1) The BUDHIES galaxies show
more asymmetric HI profiles with shallower wings compared to the UMa galaxies,
which is likely due to the environment in which they reside, (2) The
luminosity-based z=0.2 TFRs are brighter and bluer than the z=0 TFRs, even when
cluster galaxies are excluded from the BUDHIES sample, (3) The BTFR shows no
evolution in its zero point over the past 2.5 billion years and does not
significantly change on the inclusion of cluster galaxies, and (4) proper
sample selection and consistent corrections are crucial for an unbiased
analysis of the evolution of the TFR.
