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## APPENDIX A: WSRT VERSUS VLA DATA

As mentioned in the main text, two galaxies in our sample, AGC 122966 and AGC 334315, have both VLA and WSRT data. Given the spatial resolution and S/N of the data, we adopt as our 'fiducial' data the WSRT observations for AGC 122966 and the VLA observations for AGC 334315. Here, we delve into the reasons in which we based these choices, and we show the complementary data: the VLA data for AGC 122966 as well as the WSRT data for AGC 334315. We also make the comparison between the kinematic and geometrical parameters of the different data.

The VLA data cube of AGC 122966 has a lower S/N than the WSRT one. Moreover, the emission is less extended, and we have to oversample by a factor 2 in order to fit the galaxy with $^{3D}$BAROLO. Fig. A1 shows the stellar image, H I map, observed and modelled velocity fields, and PV diagrams. From inspecting the major-axis PV diagram, we can see that the emission connecting approaching and receding sides is not detected. More importantly, it looks likely that there is emission missing at the end of the approaching and residing sides too, which would significantly affect the recovered value of the rotation velocity. In fact, while for the WSRT cube $^{3D}$BAROLO finds a projected velocity of 26 km s$^{-1}$, it finds 16 km s$^{-1}$ for the VLA cube. Given all this, we decided to use the WSRT data for this galaxy (Fig. 2).

Despite the problems deriving the kinematics, we can still use the VLA data to independently estimate the inclination of the galaxy as described in the main text. Our method finds an inclination of 44° ± 5° using the WSRT H I map and of 40° ± 5° with the VLA data, meaning that the inclination estimates from the different data cubes are consistent with each other. The VLA data of AGC 122966 is not only useful to confirm our

<figure><img src="image_14.png" /><figcaption>**Figure A1.** VLA data and kinematic models for AGC 122966. Panels and symbols as in Fig. 1. The H I contours are at 0.5, 1, 2 and 4 × $10^{20}$ atoms cm$^{-2}$.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Figure A2.** WSRT data and kinematic models for AGC 334315. Panels and symbols as in Fig. 1. The H1 contours are at 0.35, 0.7, 1.4, and 2.8 × 10<sup>20</sup> atoms cm<sup>-2</sup>.</figcaption></figure>

inclination measurements, but also because the morphology of the galaxy can be better appreciated without the elongated beam of the WSRT observations (Fig. 2). Finally, the models for the different cubes have the same systemic velocity and physical centre.

On the other hand, for AGC 334315 the VLA data (Fig. 5) have better quality (although a factor 2 less extended) than the WSRT data, shown in Fig. A2: the spatial and spectral resolution are better, and the beam is more circular. With this, one can more clearly appreciate the H1 structure as well as the intrinsic shape and velocity field of the galaxy. Apart from this, the parameters found for the two different data cubes are compatible with each other: we find an inclination of 45° ± 5° for the VLA map and of 52° ± 5° with the WSRT one, in agreement within the reported uncertainties. The final circular speed is also the same within the uncertainties: 25 km s<sup>-1</sup> at 8.5 kpc for the VLA data, and 26 km s<sup>-1</sup> at 18 kpc for the WSRT observations. The models for the different cubes share also the same systemic velocity and physical centre.

# APPENDIX B: COMPARISON SAMPLES

## B1 The BTFR

Fig. 9 shows the circular speed–baryonic mass plane, with galaxies scattering around the BTFR. The main result from the figure is that the region between our extreme UDGs and galaxies following the extrapolation of the SPARC BTFR at low masses, is populated by other dwarf galaxies. When discussing specific galaxies which are particularly interesting given their position with respect to the SPARC BTFR, we provide their coordinates on the $V_{\text{circ}}-M_{\text{bar}}$ plane.

### B1.1 SPARC

Within this sample (cyan circles in Fig. 9), two galaxies deviate significantly from the SPARC BTFR: UGC 7125 (65 km s<sup>-1</sup>, 10<sup>9.86</sup> M<sub>☉</sub>) and UGC 9992 (34 km s<sup>-1</sup>, 10<sup>8.77</sup> M<sub>☉</sub>).

UGC 7125 has an inclination of 90° and $Q = 1$, so its position seems robust, even though, as Lelli et al. (2016b) mention, the galaxy has a relatively large uncertainty on its mass due to a high distance correction for Virgocentric infall.

UGC 9992 has an inclination of 30° ± 10° and $Q = 2$. Its PV diagram (Swaters 1999) is regular and traces the flat part of the rotation curve. To bring this galaxy back to the BTFR an inclination of ~ 17° would be needed. For this hypothetical inclination to be correct, an error of 13° in the measured inclination is needed, a bit larger than the quoted uncertainty of 10° but within $1.5σ$. It is worth mentioning that two other galaxies with $i = 30° ± 10°$ (F571-V1 and UGC 7261) lie much closer to the BTFR, as well as, for instance, the galaxies UGC 11914, UGC 6930, and UGC 10310, with $i = 31° ± 5°, 32° ± 5°$, and $34° ± 6°$, respectively.

### B1.2 LITTLE THINGS

Most LITTLE THINGS galaxies lie around the extrapolation of the SPARC BTFR, even when some of their rotation curves have *not* clearly reached their flat part (see Iorio et al. 2017). DDO 50 (also known as UGC 4305 or Ho II) is an outlier, in a position very close to our UDGs (39 km s<sup>-1</sup>, 10<sup>8.95</sup> M<sub>☉</sub>). Its rotation curve has clearly reached the flat part but the inclination of the galaxy is relatively low, 30°. Different values have been proposed, ranging from 30° to 50° (see Oman et al. 2016; Iorio et al. 2017, and references therein),
<figure><img src="image_15.png" /><figcaption>**Figure A2.** WSRT data and kinematic models for AGC 334315. Panels and symbols as in Fig. 1. The H1 contours are at 0.35, 0.7, 1.4, and 2.8 × 10<sup>20</sup> atoms cm<sup>-2</sup>.</figcaption></figure>

inclination measurements, but also because the morphology of the galaxy can be better appreciated without the elongated beam of the WSRT observations (Fig. 2). Finally, the models for the different cubes have the same systemic velocity and physical centre.

On the other hand, for AGC 334315 the VLA data (Fig. 5) have better quality (although a factor 2 less extended) than the WSRT data, shown in Fig. A2: the spatial and spectral resolution are better, and the beam is more circular. With this, one can more clearly appreciate the H1 structure as well as the intrinsic shape and velocity field of the galaxy. Apart from this, the parameters found for the two different data cubes are compatible with each other: we find an inclination of 45° ± 5° for the VLA map and of 52° ± 5° with the WSRT one, in agreement within the reported uncertainties. The final circular speed is also the same within the uncertainties: 25 km s<sup>-1</sup> at 8.5 kpc for the VLA data, and 26 km s<sup>-1</sup> at 18 kpc for the WSRT observations. The models for the different cubes share also the same systemic velocity and physical centre.

# APPENDIX B: COMPARISON SAMPLES

## B1 The BTFR

Fig. 9 shows the circular speed–baryonic mass plane, with galaxies scattering around the BTFR. The main result from the figure is that the region between our extreme UDGs and galaxies following the extrapolation of the SPARC BTFR at low masses, is populated by other dwarf galaxies. When discussing specific galaxies which are particularly interesting given their position with respect to the SPARC BTFR, we provide their coordinates on the $V_{\text{circ}}-M_{\text{bar}}$ plane.

### B1.1 SPARC

Within this sample (cyan circles in Fig. 9), two galaxies deviate significantly from the SPARC BTFR: UGC 7125 (65 km s<sup>-1</sup>, 10<sup>9.86</sup> M<sub>☉</sub>) and UGC 9992 (34 km s<sup>-1</sup>, 10<sup>8.77</sup> M<sub>☉</sub>).

UGC 7125 has an inclination of 90° and $Q = 1$, so its position seems robust, even though, as Lelli et al. (2016b) mention, the galaxy has a relatively large uncertainty on its mass due to a high distance correction for Virgocentric infall.

UGC 9992 has an inclination of 30° ± 10° and $Q = 2$. Its PV diagram (Swaters 1999) is regular and traces the flat part of the rotation curve. To bring this galaxy back to the BTFR an inclination of ~ 17° would be needed. For this hypothetical inclination to be correct, an error of 13° in the measured inclination is needed, a bit larger than the quoted uncertainty of 10° but within $1.5σ$. It is worth mentioning that two other galaxies with $i = 30° ± 10°$ (F571-V1 and UGC 7261) lie much closer to the BTFR, as well as, for instance, the galaxies UGC 11914, UGC 6930, and UGC 10310, with $i = 31° ± 5°, 32° ± 5°$, and $34° ± 6°$, respectively.

### B1.2 LITTLE THINGS

Most LITTLE THINGS galaxies lie around the extrapolation of the SPARC BTFR, even when some of their rotation curves have *not* clearly reached their flat part (see Iorio et al. 2017). DDO 50 (also known as UGC 4305 or Ho II) is an outlier, in a position very close to our UDGs (39 km s<sup>-1</sup>, 10<sup>8.95</sup> M<sub>☉</sub>). Its rotation curve has clearly reached the flat part but the inclination of the galaxy is relatively low, 30°. Different values have been proposed, ranging from 30° to 50° (see Oman et al. 2016; Iorio et al. 2017, and references therein),
so the exact value of its circular speed remains somewhat uncertain. However, an inclination of ~ 18° is needed for the galaxy to lie directly on the canonical BTFR, which is outside the wide range proposed in the literature.

IC 1613 (also known as DDO 8, not shown in Fig. 9), is another well-known candidate to be an outlier from the BTFR with a baryonic mass of $10^{7.9} M_{\odot}$ and rotation velocity of about 20 km s$^{-1}$ (Oh et al. 2015; Oman et al. 2016). It is part of the LITTLE THINGS galaxies studied in Oh et al. (2015), but was excluded in the work of Iorio et al. (2017). While the galaxy is potentially interesting, there may be issues with its inclination and equilibrium state, as mentioned in Read et al. (2017), Because of this, as in Iorio et al. (2017), we do not consider this galaxy in Fig. 9.

In the sample from Iorio et al. (2017), DDO 101 ($59 \text{ km s}^{-1}$, $10^{7.94} M_{\odot}$) stands out but for being an outlier that rotates too fast for its baryonic mass. However, Read et al. (2017) have demonstrated that this discrepancy is largely mitigated if the galaxy is farther away than the distance used in Iorio et al. (2017), so it is possible that the uncertainties in distance (and thus in baryonic mass) have been underestimated for this galaxy.

## B1.3 SHIELD

Due to the very low-spatial resolution data the analysis of this sample was very challenging, as discussed in McNichols et al. (2016). Five out of 12 galaxies in the sample have rotation velocities estimated from fitting tilted-ring models to the observed low-spatial resolution velocity fields, and at least three of the resulting rotation curves have no indication of a flattening. The remaining velocities were derived from the visual inspection of different PV slices (see McNichols et al. 2016 for details). In addition to this, the asymmetric drift correction was not applied to the galaxies, and the inclination comes from optical data rather than from the H1 itself. Despite these differences with other analyses, the 12 galaxies lie around the extrapolation of the canonical BTFR.

## B1.4 Edge-on HUDs

He et al. (2019) selected a sample of nearly edge-on HUDs that were not originally selected in the catalogue of L17 due to selection effects (given their high inclination the galaxies have apparent higher surface brightness). As the optical morphology indicates that the galaxies are edge-on, corrections for inclination are negligible. Their optical images, shown in He et al. (2019), suggest that their stellar structure is not exactly the same as in our sample, as theirs look more regular and thinner, but it is hard to unequivocally judge this as our sample is not edge-on. However, the stellar component of our sample is both more extended (by a factor about 2.5) and of lower surface brightness.

Most of these galaxies (magenta diamonds in Fig. 9) show velocities nearly compatible with the SPARC BTFR. The clear

outlier is AGC 202262, that shows the narrowest velocity width, with a rotation of about 30 km s$^{-1}$. An inclination of ~ 40°, totally incompatible with the optical image (but see the caveats on the optical-gas misalignment reported in Starkenburg et al. 2019 or Gault et al. submitted), would be required to put the galaxy on the canonical BTFR.

## B1.5 UGC 2162

UGC 2162 is an UDG which has been studied using $^{3D\text{BAROLO}}$ in resolved GMRT observations (Sengupta et al. 2019). Two caveats exist regarding this galaxy. First, Sengupta et al. (2019) mention that it has large uncertainties in its baryonic mass (probably because of the uncertainty associated with its distance; the galaxy is much closer than those in our sample), and second, its rotation curve does not show signs of flattening (the emission is less extended than in our data), although it is presumably close to reaching the flat part (see fig. 2 in Oman et al. 2015; Swaters et al. 1999).

While these caveats should be taken into account, the position of UGC 2162$^{11}$ in Fig. 9 (red hexagon) seems in line with our results. Note also that UGC 2162 is less ‘extreme’ than our UDGs: it is less massive, smaller, and slightly brighter. Assuming that the amplitude of the rotation curve does not increase significantly beyond the outermost measured radius, the galaxy would need an inclination of ≈ 39° to be on the SPARC BTFR, far from the measured inclination of 55° in Sengupta et al. (2019).

## B2 Disc scale length and central surface brightness values

In Fig. 10, we study the deviation from the BTFR as a function of the exponential disc scale length; the central surface brightness of the galaxies was also inspected. We have obtained these structural parameters from the following sources in the literature. For the SPARC galaxies, scale lengths are taken directly from Lelli et al. (2016a) and surface brightnesses from Verheijen (1997), de Blok (1997), and Swaters (1999). For LITTLE THINGS, scale lengths come from Read et al. (2016) and surface brightnesses from Hunter & Elmegreen (2006). Regarding SHIELD, size and surface brightness come from Teich et al. (2016) and Haurberg et al. (2015), respectively. He et al. (2019) provides both size and surface brightness for their sample, and the values used for UGC 2162 come from Trujillo et al. (2017).

<footnote>$^{11}$UGC 2162 has no reported uncertainties in rotation velocity nor H1 mass by Sengupta et al. (2019), so we assume an uncertainty of 7 km s$^{-1}$ for the velocity (the spectral resolution of the data, which is also larger than the difference in the velocity obtained from the best-fitting model of $^{3D\text{BAROLO}}$ and the global H1 profile) and a typical value of 20 per cent in the H1 mass.</footnote>

<footnote>This paper has been typeset from a TeX/LATEX file prepared by the author.</footnote>
so the exact value of its circular speed remains somewhat uncertain. However, an inclination of ~ 18° is needed for the galaxy to lie directly on the canonical BTFR, which is outside the wide range proposed in the literature.

IC 1613 (also known as DDO 8, not shown in Fig. 9), is another well-known candidate to be an outlier from the BTFR with a baryonic mass of $10^{7.9} M_{\odot}$ and rotation velocity of about 20 km s$^{-1}$ (Oh et al. 2015; Oman et al. 2016). It is part of the LITTLE THINGS galaxies studied in Oh et al. (2015), but was excluded in the work of Iorio et al. (2017). While the galaxy is potentially interesting, there may be issues with its inclination and equilibrium state, as mentioned in Read et al. (2017), Because of this, as in Iorio et al. (2017), we do not consider this galaxy in Fig. 9.

In the sample from Iorio et al. (2017), DDO 101 (59 km s$^{-1}$, $10^{7.94} M_{\odot}$) stands out but for being an outlier that rotates too fast for its baryonic mass. However, Read et al. (2017) have demonstrated that this discrepancy is largely mitigated if the galaxy is farther away than the distance used in Iorio et al. (2017), so it is possible that the uncertainties in distance (and thus in baryonic mass) have been underestimated for this galaxy.

## B1.3 SHIELD

Due to the very low-spatial resolution data the analysis of this sample was very challenging, as discussed in McNichols et al. (2016). Five out of 12 galaxies in the sample have rotation velocities estimated from fitting tilted-ring models to the observed low-spatial resolution velocity fields, and at least three of the resulting rotation curves have no indication of a flattening. The remaining velocities were derived from the visual inspection of different PV slices (see McNichols et al. 2016 for details). In addition to this, the asymmetric drift correction was not applied to the galaxies, and the inclination comes from optical data rather than from the H1 itself. Despite these differences with other analyses, the 12 galaxies lie around the extrapolation of the canonical BTFR.

## B1.4 Edge-on HUDs

He et al. (2019) selected a sample of nearly edge-on HUDs that were not originally selected in the catalogue of L17 due to selection effects (given their high inclination the galaxies have apparent higher surface brightness). As the optical morphology indicates that the galaxies are edge-on, corrections for inclination are negligible. Their optical images, shown in He et al. (2019), suggest that their stellar structure is not exactly the same as in our sample, as theirs look more regular and thinner, but it is hard to unequivocally judge this as our sample is not edge-on. However, the stellar component of our sample is both more extended (by a factor about 2.5) and of lower surface brightness.

Most of these galaxies (magenta diamonds in Fig. 9) show velocities nearly compatible with the SPARC BTFR. The clear

outlier is AGC 202262, that shows the narrowest velocity width, with a rotation of about 30 km s$^{-1}$. An inclination of ~ 40°, totally incompatible with the optical image (but see the caveats on the optical-gas misalignment reported in Starkenburg et al. 2019 or Gault et al. submitted), would be required to put the galaxy on the canonical BTFR.

## B1.5 UGC 2162

UGC 2162 is an UDG which has been studied using $^{3D}$BAROLO in resolved GMRT observations (Sengupta et al. 2019). Two caveats exist regarding this galaxy. First, Sengupta et al. (2019) mention that it has large uncertainties in its baryonic mass (probably because of the uncertainty associated with its distance; the galaxy is much closer than those in our sample), and second, its rotation curve does not show signs of flattening (the emission is less extended than in our data), although it is presumably close to reaching the flat part (see fig. 2 in Oman et al. 2015; Swaters et al. 1999).

While these caveats should be taken into account, the position of UGC 2162$^{11}$ in Fig. 9 (red hexagon) seems in line with our results. Note also that UGC 2162 is less 'extreme' than our UDGs: it is less massive, smaller, and slightly brighter. Assuming that the amplitude of the rotation curve does not increase significantly beyond the outermost measured radius, the galaxy would need an inclination of ≈ 39° to be on the SPARC BTFR, far from the measured inclination of 55° in Sengupta et al. (2019).

## B2 Disc scale length and central surface brightness values

In Fig. 10, we study the deviation from the BTFR as a function of the exponential disc scale length; the central surface brightness of the galaxies was also inspected. We have obtained these structural parameters from the following sources in the literature. For the SPARC galaxies, scale lengths are taken directly from Lelli et al. (2016a) and surface brightnesses from Verheijen (1997), de Blok (1997), and Swaters (1999). For LITTLE THINGS, scale lengths come from Read et al. (2016) and surface brightnesses from Hunter & Elmegreen (2006). Regarding SHIELD, size and surface brightness come from Teich et al. (2016) and Haurberg et al. (2015), respectively. He et al. (2019) provides both size and surface brightness for their sample, and the values used for UGC 2162 come from Trujillo et al. (2017).

<footnote>$^{11}$UGC 2162 has no reported uncertainties in rotation velocity nor H I mass by Sengupta et al. (2019), so we assume an uncertainty of 7 km s$^{-1}$ for the velocity (the spectral resolution of the data, which is also larger than the difference in the velocity obtained from the best-fitting model of $^{3D}$BAROLO and the global H I profile) and a typical value of 20 per cent in the H I mass.</footnote>

<footnote>This paper has been typeset from a TeX/LATEX file prepared by the author.</footnote>