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)
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