Three non-intersecting strings in two dimensions which interact via short-ranged attractive potentials are studied using both transfer matrix methods and Monte Carlo techniques. The critical behavior at thé unbinding transition and thé critical values of thé potential strength are determined for symmetric and asymmetric bundles of strings. In thé asymmetric case, for which thé two outer strings have différent line tensions (or interact via différent potentials), thé strings unbind in two subséquent transitions, which then exhibit universal critical behavior. In thé symmetric case, where thé two outer strings have thé same line tension, thé three strings unbind simultaneously. The critical behavior at this unbinding transition is found to be non-universal for thé whole range of accessible length scales, but its parameter dependence is found to be in strong disagreement with thé prédictions of thé so-called necklace model. The more flexible thé inner string, thé deeper thé critical potential. However, within thé numerical error, three identical strings are found to unbind at thé same critical potential strength as two strings with thé same line tensions