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Prompt D meson and non-prompt J/ yields are studied as a function of the multiplicity of charged particles produced in inelastic proton-proton collisions at a centre-of-mass energy of TeV. The results are reported as a ratio between yields in a given multiplicity interval normalised to the multiplicity-integrated ones (relative yields). They are shown as a function of the multiplicity of charged particles normalised to the average value for inelastic collisions (relative charged-particle multiplicity). D, D and D mesons are measured in five intervals from 1 to 20 GeV/ and for via their hadronic decays. The D-meson relative yield is found to increase with increasing charged-particle multiplicity. For events with multiplicity six times higher than the average multiplicity of inelastic collisions, a yield enhancement of a factor about 15 relative to the multiplicity-integrated yield in inelastic collisions is observed. The yield enhancement is independent of transverse momentum within the uncertainties of the measurement. The D-meson relative yield is also measured as a function of the relative multiplicity at forward pseudorapidity. The non-prompt J/, i.e. the B hadron, contribution to the inclusive J/ production is measured in the di-electron decay channel at central rapidity. It is evaluated for GeV/ and , and extrapolated to . The fraction of non-prompt J/ in the inclusive J/ yields shows no dependence on the charged-particle multiplicity at central rapidity. Charm and beauty hadron relative yields exhibit a similar increase with increasing charged-particle multiplicity. The measurements are compared to PYTHIA 8, EPOS 3 and percolation calculations.