Random sequential adsorption of extended objects deposited on two-dimensional regular lattices is studied. The depositing objects are chains formed by occupying adsorption sites on the substrate through a self-avoiding walk of k lattice steps; these objects are also called “tortuous k-mers.” We study how the jamming coverage, θj,k , depends on k for lattices with different connectivity (honeycomb, square, and triangular). The dependence can be fitted by the function θj,k = θj,k→∞ + B/k + C/k2, where B and C are found to be shared parameters by the three lattices and θj,k→∞ (>0) is the jamming coverage for infinitely long k-mers for each of them. The jamming coverage is found to have a growing behavior with the connectivity of the lattice. In addition, θj,k is found to be higher for tortuous k-mers than for the previously reported for linear k-mers in each lattice. The results were obtained by means of numerical simulation through an efficient algorithm whose characteristics are discussed in detail. The computational method introduced here also allows us to investigate the full-time kinetics of the surface coverage θk (t) [θj,k ≡ θk (t → ∞)]. Along this line, different time regimes are identified and characterized