We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth U and width W is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value Uc corresponding to the adsorption transition scales as W−1/ν , where the exponent ν = 1/2 for ideal chains and ν ≈ 3/5 for self-avoiding walks. Lattice corrections for finite W are incorporated in the analytical prediction of the ideal chain theory Uc ≈ ( π2 24 )(W + 1/2)−2 and in the best-fit equation for the MC simulation data Uc = 0.585(W + 1/2)−5/3. Tail, loop, and train distributions at the critical point are evaluated by MC simulations for 1 W 10 and compared to analytical results for ideal chains and with scali