We present a comparative density functional tight binding study of an organic molecule attachment to TiO2 via a carboxylic group, with the example of acetic acid. For the first time, binding to low-energy surfaces of crystalline anatase (101), rutile (110) and (B)-TiO2 (001), as well as to the surface of amorphous (a-) TiO2 is compared with the same computational setup. On all surfaces, bidentate configurations are identified as providing the strongest adsorption energy, Eads = -1.93, -2.49 and -1.09 eV for anatase, rutile and (B)-TiO2, respectively. For monodentate configurations, the strongest Eads = -1.06, -1.11 and -0.86 eV for anatase, rutile and (B)-TiO2, respectively. Multiple monodentate and bidentate configurations are identified on a-TiO2 with a distribution of adsorption energies and with the lowest energy configuration having stronger bonding than that of the crystalline counterparts, with Eads up to -4.92 eV for bidentate and -1.83 eV for monodentate adsorption. Amorphous TiO2 can therefore be used to achieve strong anchoring of organic molecules, such as dyes, that bind via a -COOH group. While the presence of the surface leads to a contraction of the band gap vs. the bulk, molecular adsorption caused no appreciable effect on the band structure around the gap in any of the systems.