Hot melt adhesive compositions containing hyper-branched SBS block copolymers and end use applications thereof. The hyper-branched SBS is characterized in having a ratio between light-scattering molecular weight (of non-di-block polymer) and GPC molecular weight (of non-di-block polymer) greater than 1.4 and having ratio between light scattering molecular weight molecular weight (of non-di-block polymer) and light scattering molecular weight molecular weight (of di-block polymer) greater than 5. The ratio between light scattering molecular weight MW (of non-di-block polymer) and light scattering molecular weight MW (of di-block polymer) also defines the number of arms for the hyper branched structure. The weight average molecular weight of each arm of the hyper-branched SBS block copolymer is less than about 100,000. These are multipurpose adhesives finding utility as packaging, labeling, construction and positioning adhesives, and are particularly well suited for use as elastic attachment adhesives in the manufacture of elastic-containing products, such as disposable absorbent elastic articles.