  We introduce a new stick-breaking construction for inhomogeneous continuum
random trees (ICRT). This new construction allows us to prove the necessary and
sufficient condition for compactness conjectured by Aldous, Miermont and Pitman
arXiv:math/0401115 by comparison with L\'evy trees. We also compute the fractal
dimensions (Minkowski, Packing, Hausdorff).

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