I. Agulli, J. A. Aguerri, and R. Sánchez-janssen, MNRAS, vol.444, p.34, 2014.

H. Aihara, R. Armstrong, and S. Bickerton, PASJ, 2017.

N. C. Amorisco and A. Loeb, MNRAS, vol.459, p.51, 2016.

N. C. Amorisco, A. Monachesi, and S. D. White, , 2016.

S. Andreon and M. A. Hurn, MNRAS, vol.404, p.1922, 2010.

M. A. Beasley and I. Trujillo, ApJ, vol.830, p.23, 2016.

M. A. Beasley, A. J. Romanowsky, and V. Pota, ApJ, vol.819, p.20, 2016.

E. Bertin and S. Arnouts, A&AS, vol.117, p.393, 1996.

M. R. Blanton, D. W. Hogg, and N. A. Bahcall, ApJ, vol.592, p.819, 2003.

J. M. Budzynski, S. E. Koposov, I. G. Mccarthy, and V. Belokurov, MNRAS, vol.437, p.1362, 2014.

J. J. Dalcanton, D. N. Spergel, J. E. Gunn, M. Schmidt, and D. P. Schneider, AJ, vol.114, p.635, 1997.

L. J. Davies, A. S. Robotham, and S. P. Driver, MNRAS, vol.455, p.4013, 2016.

J. T. De-jong, G. A. Verdoes-kleijn, and D. R. Boxhoorn, A&A, vol.582, p.62, 2015.

J. T. De-jong, G. A. Verdoes-kleijn, and T. Erben, A&A, vol.604, p.134, 2017.

R. De-propris, S. Phillipps, and M. N. Bremer, MNRAS, vol.434, p.3469, 2013.

A. Di-cintio, C. B. Brook, and A. A. Dutton, MNRAS, vol.466, p.1, 2017.

S. P. Driver, D. T. Hill, and L. S. Kelvin, MNRAS, vol.413, p.971, 2011.

A. R. Duffy, J. Schaye, S. T. Kay, and C. Vecchia, MNRAS, vol.390, p.64, 2008.

A. A. Dutton and A. V. Macciò, MNRAS, vol.441, p.3359, 2014.

T. Erben, H. Hildebrandt, and L. Miller, MNRAS, vol.433, p.2545, 2013.

A. E. Evrard, J. Bialek, and M. Busha, ApJ, vol.672, p.122, 2008.

A. H. Gonzalez, S. Sivanandam, A. I. Zabludoff, and D. Zaritsky, ApJ, vol.778, p.14, 2013.

R. E. González, A. V. Kravtsov, and N. Y. Gnedin, ApJ, vol.793, p.91, 2014.

P. Hickson, ApJ, vol.255, p.382, 1982.

H. Hildebrandt, M. Viola, and C. Heymans, MNRAS, vol.465, p.1454, 2017.

C. Impey, G. Bothun, and D. Malin, ApJ, vol.330, p.634, 1988.

S. Janssens, R. Abraham, and J. Brodie, ApJ, vol.839, p.17, 2017.

J. Kadowaki, D. Zaritsky, and R. L. Donnerstein, ApJ, vol.838, p.21, 2017.

C. S. Kochanek, M. White, and J. Huchra, ApJ, vol.585, p.161, 2003.

J. Koda, M. Yagi, H. Yamanoi, and Y. Komiyama, ApJ, vol.807, p.2, 2015.

K. Kuijken, C. Heymans, and H. Hildebrandt, MNRAS, vol.454, p.3500, 2015.

T. F. Laganá, N. Martinet, and F. Durret, A&A, vol.555, p.66, 2013.

Y. Lin, J. J. Mohr, and S. A. Stanford, ApJ, vol.610, p.745, 2004.

J. Liske, I. K. Baldry, and S. P. Driver, MNRAS, vol.452, p.2087, 2015.

C. Marinoni and M. J. Hudson, ApJ, vol.569, p.101, 2002.

C. Mendes-de-oliveira, P. Coelho, J. J. González, and B. Barbuy, AJ, vol.130, p.55, 2005.

A. Merritt, P. Van-dokkum, and S. Danieli, ApJ, vol.833, p.168, 2016.

J. C. Mihos, P. R. Durrell, and L. Ferrarese, ApJ, vol.809, p.21, 2015.

R. P. Muñoz, P. Eigenthaler, and T. H. Puzia, ApJ, vol.813, p.15, 2015.

A. Muzzin, H. K. Yee, P. B. Hall, and H. Lin, ApJ, vol.663, p.150, 2007.

J. F. Navarro, C. S. Frenk, and S. D. White, ApJ, vol.490, p.493, 1997.

E. W. Peng and S. Lim, ApJ, vol.822, p.31, 2016.

C. Y. Peng, L. C. Ho, C. D. Impey, and H. Rix, AJ, vol.124, p.266, 2002.

P. Popesso, H. Böhringer, M. Romaniello, and W. Voges, A&A, vol.433, p.415, 2005.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 1992.

R. N. Proctor, D. A. Forbes, and G. K. Hau, MNRAS, vol.349, p.1381, 2004.

K. Rines, M. J. Geller, A. Diaferio, M. J. Kurtz, and T. H. Jarrett, AJ, vol.128, p.1078, 2004.

A. S. Robotham, P. Norberg, and S. P. Driver, MNRAS, vol.416, p.2640, 2011.

J. Román and I. Trujillo, MNRAS, vol.468, p.703, 2017.

J. Román and I. Trujillo, MNRAS, vol.468, p.4039, 2017.

Y. Rong, Q. Guo, and L. Gao, MNRAS, vol.470, p.4231, 2017.

C. Sifón, H. Hoekstra, and M. Cacciato, A&A, vol.575, p.48, 2015.

C. Sifón, R. F. Van-der-burg, H. Hoekstra, A. Muzzin, and R. Herbonnet, MNRAS, 2017.

J. Silk, ApJ, vol.839, p.13, 2017.

J. A. Turner, S. Phillipps, J. I. Davies, M. J. Disney, R. F. Van-der-burg et al., MNRAS, vol.261, p.43, 1993.

M. Viola, M. Cacciato, and M. Brouwer, MNRAS, vol.452, p.3529, 2015.

R. P. Williams, I. K. Baldry, and L. S. Kelvin, MNRAS, vol.463, p.2746, 2016.

M. Yagi, J. Koda, Y. Komiyama, and H. Yamanoi, ApJS, vol.225, p.11, 2016.

C. Yozin and K. Bekki, MNRAS, vol.452, p.937, 2015.

D. Zaritsky, L110 directly measured in the highest-z groups because their angular sizes are then smaller than 1 . 5. The fitted power-law size distribution thus already enters into the correction factor. Moreover, we normalised the distribution here per, MNRAS, vol.464, 2017.

, Since the number of UDGs is a strong function of the halo mass (cf. 3), primarily probing high-mass haloes at high redshift would introduce an artificial tilt in the measured relation. To circumvent this, we scaled the UDG numbers by dividing them over M 1.1 200 . Again, if we were to probe the same halo mass distribution at different redshifts

, 200 (i.e. 3? higher or lower than the fiducial model), we find ?2.70 ± 0.34 and ?2.70 ± 0.33, respectively. Uncertainties in the assumed abundance-mass distribution thus have a negligible effect on the measured size distribution