“…Without better terms, and to avoid repeatedly listing "Asia, Africa and Latin America" throughout the paper, I use the imperfect and certainly not neutral spatial constructs of the (global) south and north (cf Bhan et al, 2018;Mohan et al, 2021; . Parnell & Oldfield, 2014).2 For more details seeSimon et al (2006).3 I adopt the idea of "conceptual vectors" fromRoy (2009) andErnstson et al (2014).4 A more detailed debate about the concept of urbanization is beyond the scope of this paper (see, e.g.,Harvey, 1996;Brenner & Schmid, 2015;Davidson & Iveson, 2015).5 I chose these excellent peri-urban studies not to denounce, but rather to highlight how highly influential and thoughtful work on peri-urbanization has, so far, largely disregarded the questions of what distinguishes peri-urbanization from urbanization.6 I borrow the terminology of "not-quite-urban" fromLawhon (2020, p. 39).7 I am grateful to the anonymous reviewer suggesting this terminology, which perfectly describes this understanding.8 Suburbanization is generally understood as "the combination of non-centric population and economic growth with urban spatial expansion"(De Vidovich, 2019, p. 2, based upon Hamel & Keil, 2015.9 "(1) the speculative periphery;(2) the vanguard periphery;(3) the auto-constructed periphery; (4) the transitioning periphery; and (5) the inherited periphery"(Meth et al, 2021) …”