We have identified 453 compact dense cores in 3 mm continuum emission maps in the ALMA Three-millimetre Observations of Massive Star-forming regions survey, and compiled three catalogues of high-mass star-forming cores. One catalogue, referred to as hyper/ultra compact (H/UC)-H II catalogue, includes 91 cores that enshroud H/UC H II regions as characterized by associated compact H40{alpha} emission. A second catalogue, referred to as pure s-cHMC, includes 31 candidate hot molecular cores (HMCs) showing rich spectra (N >= 20 lines) of complex organic molecules (COMs) and not associated with H/UC-H ii regions. The third catalogue, referred to as pure w-cHMC, includes 51 candidate HMCs with relatively low levels of COM richness and not associated with H/UC-H II regions. These three catalogues of dense cores provide an important foundation for future studies of the early stages of high-mass star formation across the Milky Way. We also find that nearly half of H/UC-H II cores are candidate HMCs. From the number counts of COM-containing and H/UC-H II cores, we suggest that the duration of high-mass protostellar cores showing chemically rich features is at least comparable to the lifetime of H/UC-H II regions. For cores in the H/UC-H II catalogue, the width of the H40{alpha} line increases as the core size decreases, suggesting that the non-thermal dynamical and/or pressure line-broadening mechanisms dominate on the smaller scales of the H/UC-H II cores.