Liquid chromatography at the critical condition (LCCC) has been used to characterize graft copolymers based on the assumption that one of the copolymer blocks becomes chromatographically "invisible" at the critical condition of the corresponding homopolymer. We investigate the validity of this assumption with lattice Monte Carlo simulations of A-g-B graft copolymers modeled as either random walk (RW) or self-avoiding walk (SAW) chains composed of multiple invisible B blocks grafted to an A backbone that is either in size-exclusion chromatography (SEC) or liquid adsorption chromatography (LAC) mode. The simulations show that, in agreement with recent experimental results, the B blocks have a small, but noticeable, impact on the overall elution of the graft copolymer. This influence exists even when the chains are modeled as RWs, indicating that its fundamental origin is due to chain connectivity, not excluded volume interactions. In general, both models show that grafting B blocks to an A backbone in SEC mode tends to increase copolymer retention, while grafting B blocks to an A backbone in LAC mode tends to decrease copolymer retention. When the copolymer is modeled as a SAW, the excluded volume interaction increases the entropic penalty associated with the addition of a B block and, therefore, the addition of B blocks in SAW chains is more likely to result in a decrease in the retention time of the copolymer when the A backbone is in LAC mode. (C) 2015 Elsevier Ltd. All rights reserved.