An apparatus is provided wherein web material is unwound from successive rolls of web material by imparting a constant draw in the web material. The web is then forwarded through a constant tension zone to downstream equipment such as a converter for manufacturing disposable absorbent products. The constant tension zone is provided to isolate the web being forwarded under constant tension from tension fluctuations which may occur in the constant draw unwind portion of the apparatus: such tension fluctuations being relatively large in magnitude and random in nature especially with net-like webs, and blocking prone web marterials. A splicer is provided in the constant tension zone in close proximity to the constant-draw unwind to effect splices near the tail end of a just depleted roll of web but prior to the tail end passing out of the constant-draw unwind portion of the apparatus. Additionally, the apparatus is slaved to the downstream equipment so that it responds in timed relation with changes made in the speed of the downstream equipment.