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Studies of extra-galactic globular clusters have shown that the peak size ofthe globular cluster (GC) radius distribution (RD) depends only weakly ongalactic environment, and can be used as a standard ruler. We model RDs of GCpopulations using a simple prescription for a Hubble time of relaxation drivenevolution of cluster mass and radius, and explore the conditions under whichthe RD can be used as a standard ruler. We consider a power-law cluster initialmass function (CIMF) with and without an exponential truncation, and focus inparticular on a flat and a steep CIMF (power-law indices of 0 and -2,respectively). For the initial half-mass radii at birth we adopt eitherRoche-lobe filling conditions ('filling',meaning that the ratio of half-mass toJacobi radius is approximately rh/rJ ~ 0.15) or strongly Roche-lobeunder-filling conditions ('under-filling', implying that initially rh/rJ <<0.15). Assuming a constant orbital velocity about the galaxy centre we find fora steep CIMF that the typical half-light radius scales with galactocentricradius RG as RG^1/3. This weak scaling is consistent with observations, butthis scenario has the (well known) problem that too many low-mass clusterssurvive. A flat CIMF with 'filling' initial conditions results in the correctmass function at old ages, but with too many large (massive) clusters at largeRG. An 'underfilling' GC population with a flat CIMF also results in thecorrect mass function, and can also successfully reproduce the shape of the RD,with a peak size that is (almost) independent of RG. In this case, the peaksize depends (almost) only on the peak mass of the GC mass function. The (near)universality of the GC RD is therefore because of the (near) universality ofthe CIMF. There are some extended GCs in the outer halo of the Milky Way thatcannot be explained by this model.

Constraining the initial conditions of globular clusters using their radius distribution