Improved object wrapping materials exhibiting a number of beneficial properties to overcome prior deficiencies are provided. Such properties include the inclusion of a separation interface overlay that allows for greater rigidity at the leading and trailing edges of such wraps. Also, the inclusion of shear-reducing wrap material portions is described, as well as recoil reduction structures within the leading edge regions. Furthermore, core adhesive additions allow for greater resiliency to the base wrap material as it unwinds therefrom, reducing potential waste wrap products by permitting greater amounts of wrap materials in use. Other considerations include the ability, through proper configuration designs, to position a wrap separation indicator within a certain range of distances from the trailing edge, thereby providing greater reliability of wrap application device disengagement during wrap application. Such benefits are thus supplied individually and in tandem for improved versatility and utility of suc
