End effects are known to play a pivotal role in equilibrium polymerization. To investigate their role in detail, we apply constraints to the first and last bonds of model linear aggregates that exhibit a helix-coil type configurational transition. Three different classes of behavior manifest themselves. These can be distinguished by the presence or absence of re-entrance behavior of nonhelical conformations at constant helical-bond strength, as well as by the dependence of the locations of the polymerization and helical transitions on the cooperativity of the helical transition. A comparison of the theory with experimental data on solutions of chiral discotic molecules in n-butanol shows that only one of the three classes can account for the experimental observations.