  We present the largest catalogue of HI single dish observations of isolated
galaxies to date and the corresponding HI scaling relations, as part of the
multi-wavelength project AMIGA (Analysis of the interstellar Medium in Isolated
GAlaxies). Despite numerous studies of the HI content of galaxies, no revision
has been made for the most isolated L* galaxies since 1984. In total we have
measurements or constraints on the HI masses of 844 galaxies from the Catalogue
of Isolated Galaxies (CIG), obtained with our own observations at Arecibo,
Effelsberg, Nancay and GBT, and spectra from the literature. Cuts are made to
this sample to ensure isolation and a high level of completeness. We then fit
HI scaling relations based on luminosity, optical diameter and morphology. Our
regression model incorporates all the data, including upper limits, and
accounts for uncertainties in both variables, as well as distance
uncertainties. The scaling relation of HI mass with optical diameter is in good
agreement with that of Haynes & Giovanelli 1984, but our relation with
luminosity is considerably steeper. This is attributed to the large
uncertainties in the luminosities, which introduce a bias when using OLS
regression (used previously), and the different morphology distributions of the
samples. We find that the main effect of morphology on the relations is to
increase the intercept and flatten the slope towards later types. These trends
were not evident in previous works due to the small number of detected
early-type galaxies. The HI scaling relations of the AMIGA sample define an
up-to-date metric of the HI content of almost "nurture free" galaxies. These
relations allow the expected HI mass, in the absence of interactions, of a
galaxy to be predicted to within 0.25 dex, and are thus suitable for use as
statistical measures of the impact of interactions on the neutral gas content
of galaxies. (Abridged)
