TF. Traditionally, the velocity at a galactocentric radius $r=2.2R_{\rm D}$, where $R_{\rm D}$ is the exponential stellar disk scale-length, has often been used to build the TF relation from observations. This velocity roughly corresponds to the peak velocity of a bulgeless disk; in the case of a galaxy with a substantial bulge however, the region around $r=2.2R_{\rm D}$ contains a different mix of dark matter, gas and stars, and the peak of the rotation curve is actually at a different radius.

Following Tonini et al. (2011), we adopt a *dynamical* definition of the disk scale-length, that corresponds to a *fixed angular momentum* rather than a fixed galactocentric distance. With this definition the value of $R_{\rm D}$ self-regulates in the presence of a bulge. The formation of the bulge, both from secular evolution and mergers, implies that stars migrate radially or with inspiralling orbits to the centre of the galaxy, losing all their angular momentum and settling into a pressure-supported configuration. This lost angular momentum is transferred to the disk (Dutton et al. 2007; see also Tonini et al. 2006), with the net effect of increasing the disk size. For a bulge of mass $M_{\rm bulge}$ forming in a disk of 