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The measurement of Υ(1S), Υ(2S), and Υ(3S) yields as a function of the charged-particle multiplicity density, dNch/dη, using the ALICE experiment at the LHC, is reported in pp collisions at s√= 13 TeV. The Υ meson yields are measured at forward rapidity (2.5<y<4) in the dimuon decay channel, whereas the charged-particle multiplicity is defined at central rapidity (|η|<1). Both quantities are divided by their average value in minimum bias events to compute the self-normalized quantities. The increase of the self-normalized Υ(1S), Υ(2S), and Υ(3S) yields is found to be compatible with a linear scaling with the self-normalized dNch/dη, within the uncertainties. The self-normalized yield ratios of excited-to-ground Υ states are compatible with unity within uncertainties. Similarly, the measured double ratio of the self-normalized Υ(1S) to the self-normalized J/ψ yields, both measured at forward rapidity, is compatible with unity for self-normalized charged-particle multiplicities beyond one. The measurements are compared with theoretical predictions incorporating initial or final state effects.