  We present the results of a study of the host galaxies of high redshift Type
Ia supernovae (SNe Ia). We provide a catalog of 18 hosts of SNe Ia observed
with the Hubble Space Telescope (HST) by the High-z Supernova Search Team
(HZT), including images, scale-lengths, measurements of integrated (Hubble
equivalent) BVRIZ photometry in bands where the galaxies are brighter than m ~
25 mag, and galactocentric distances of the supernovae. We compare the
residuals of SN Ia distance measurements from cosmological fits to measurable
properties of the supernova host galaxies that might be expected to correlate
with variable properties of the progenitor population, such as host galaxy
color and position of the supernova. We find mostly null results; the current
data are generally consistent with no correlations of the distance residuals
with host galaxy properties in the redshift range 0.42 < z < 1.06. Although a
subsample of SN hosts shows a formally significant (3-sigma) correlation
between apparent V-R host color and distance residuals, the correlation is not
consistent with the null results from other host colors probed by our largest
samples. There is also evidence for the same correlations between SN Ia
properties and host type at low redshift and high redshift. These similarities
support the current practice of extrapolating properties of the nearby
population to high redshifts pending more robust detections of any correlations
between distance residuals from cosmological fits and host properties.
