The optical and near-infrared Tully-Fisher relations are examined for an HI-selected sample of galaxies. This sample is unique in that membership is simply defined by the overlap of blind 21-cm, optical and near-infrared catalogues, rather than pre-selecting candidate Tully Fisher galaxies for which to obtain rotational measurements. Three fundamental questions are considered: (i) Does the scatter depend on a third variable? (ii) What is the intrinsic scatter of the relationship? (iii) What is the slope of the z = 0 relationship as a function of wavelength, and can a single slope relationship be obtained by converting to stellar or baryonic mass? The H I Parkes All-Sky Survey (HIPASS) Catalogue (HICAT) provides 21-cm linewidths for 4315 galaxies selected purely on their HI content, and enables the Tully-Fisher relation to be studied without the need to optically pre-select galaxies for which to obtain rotational measures. ESO-LV and the Two Micron All-Sky Survey (2MASS) are used for optical (B, R) and near-infrared (J, H, K) photometry, with samples of up to 351 and 860 galaxies examined, respectively.Third parameter dependencies are tested by correlating offsets from the derived B-and K-band relations with candidate observed and intrinsic variables. A strong dependence is found on purely observational parameters such as galaxy inclination and size. Large-scale galaxy flows are also found to increase observed scatter. Correlations of Tully-Fisher offset with physical properties are found to be strongly dependent on the fitted slope of relation, indicating that if real, these dependencies are weak and largely act in parallel to the observed relations. However, a potential dependence is observed on stellar population (as measured by B-R colour) and star formation rate (measured by far-infrared luminosity).The intrinsic scatter and slope of the Tully-Fisher relation are measured by applying galaxy selection cuts to minimize observational errors. For the B-band relation, a slope of 3.40 +/- 0.09 is obtained with an observed scatter of 0.40mag (intrinsic 0.33 mag), and for the K-band relation a slope of 3.75 +/- 0.08 is found with an observed scatter of 0.33 mag (intrinsic 0.25 mag). Including the observed HI masses to calculate baryonic relations, a slope of 3.91 +/- 0.13 is obtained in B and 4.35 +/- 0.14 in K.