  We study geometric random graphs defined on the points of a Poisson process
in $d$-dimensional space, which additionally carry independent random marks.
Edges are established at random using the marks of the endpoints and the
distance between points in a flexible way. Our framework includes the soft
Boolean model (where marks play the role of radii of balls centred in the
vertices), a version of spatial preferential attachment (where marks play the
role of birth times), and a whole range of other graph models with scale-free
degree distributions and edges spanning large distances. In this versatile
framework we give sharp criteria for absence of ultrasmallness of the graphs
and in the ultrasmall regime establish a limit theorem for the chemical
distance of two points. Other than in the mean-field scale-free network models
the boundary of the ultrasmall regime depends not only on the power-law
exponent of the degree distribution but also on the spatial embedding of the
graph, quantified by the rate of decay of the probability of an edge connecting
typical points in terms of their spatial distance.
