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Percolation model with nucleation and object growth is studied by Monte Carlo simulations on a triangular lattice with point-like impurities. Growing objects are needle-like objects and self-avoiding random walk chains. In each run through the system the lattice is initially randomly occupied by point-like impurities at given concentration ρ i m p . Then the seeds for the object growth are randomly distributed at given concentration ρ. The percolation properties and the jamming densities are compared for the two classes of growing objects on the basis of the results obtained for a wide range of densities ρ and ρ i m p up to the percolation threshold for the monomer deposition on a triangular lattice. Values of the percolation thresholds θ p ∗ have lower values for the needle-like objects than for the self-avoiding random walk chains. The difference is largest for the lowest values of ρ and ρ i m p , and ceases near the values of the site percolation threshold for monomers on the triangular lattice, ρ p ∗ ≃ 0.5 . Values of the jamming coverage θ J decrease with ρ i m p for given ρ. This effect is more prominent for the growing random walk chains. © 2023 IOP Publishing Ltd and SISSA Medialab srl