This paper explores the quantitative connection between globular clusters and the 'diffuse' stellar population of the galaxies they are associated with. Both NGC 1399 and NGC 4486 (M87) are well suited for this kind of analysis due to their large globular cluster populations. The main assumption of our Monte Carlo based models is that each globular cluster is formed along with a given diffuse stellar mass that shares the same spatial distribution, chemical composition and age. The main globular cluster subpopulations, that determine the observed bimodal colour distribution, are decomposed avoiding a priori parametric (e.g. Gaussian) fits and using a new colour (C - T 1)-metallicity relation. The eventual detectability of a 'blue' tilt in the colour-magnitude diagrams of the blue globular cluster subpopulation is also addressed. A successful link between globular clusters and the stellar galaxy halo is established by assuming that the number of globular clusters per associated diffuse stellar mass t is a function of total abundance [Z/H] and behaves as t = γ exp(-δ[Z/H]) (i.e. increases when abundance decreases). The simulations allow the prediction of a surface brightness profile for each galaxy through these two free parameters' approximation. The γ, δ parameters that provide the best fit to the observed profiles in the B band, in turn, determine several features, namely, large-scale halo colour gradients, globular cluster-halo colour offset, clusters' cumulative specific frequencies, and stellar metallicity distributions, that compare well with observations. The results suggest the co-existence of two distinct stellar populations characterized by widely different metallicities and spatial distributions. One of these populations (connected with the blue globular clusters) is metal poor, highly homogeneous, exhibits an extended spatial distribution and becomes more evident at large galactocentric radius contributing with some 20 per cent of the total stellar mass. In turn, the stellar population associated with the red globular clusters is extremely heterogeneous and dominates the inner region of both galaxies. Remarkably, and although the cluster populations of these galaxies exhibit detectable differences in colour distribution, the δ parameter that determines the shape of the brightness profiles of both galaxies has the same value, δ ≈ 1.1 to 1.2 ± 0.1.Facultad de Ciencias Astronómicas y Geofísica
