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We consider the production of 𝑍 bosons associated with a heavy (charm and beauty) jet at the LHC energies using two scenarios based on the transverse momentum dependent (TMD) parton densities in the proton. First of them employs the Catani-Ciafaloni-Fiorani-Marchesini gluon evolution and is implemented into the Monte-Carlo event generator PEGASUS. The second scheme is based on the Parton Branching approach implemented into the Monte-Carlo event generator CASCADE. We compare the predictions obtained within these two TMD-based approaches with each other, investigate their sensitivity to the TMD gluon densities in the proton and estimate the effects coming from parton showers, double parton scattering mechanism and possible intrinsic charm. Additionally, we compare our predictions with the results of traditional (collinear) pQCD calculations performed with the NLO accuracy. It is shown that the TMD-based results do not contradict LHC experimental data.