We consider transition amplitudes in the coloured simplicial Boulatov model
    for three-dimensional Riemannian quantum gravity. First, we discuss aspects of
    the topology of coloured graphs with non-empty boundaries. Using a modification
    of the standard rooting procedure of coloured tensor models, we then write
    transition amplitudes systematically as topological expansions. We analyse the
    transition amplitudes for the simplest boundary topology, the 2-sphere, and
    prove that they factorize into a sum entirely given by the combinatorics of the
    boundary spin network state and that the leading order is given by graphs
    representing the closed 3-ball in the large N limit. This is the first step
    towards a more detailed study of the holographic nature of coloured
    Boulatov-type GFT models for topological field theories and quantum gravity.

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