Thats incorrect, while the World Heavyweight Championship is pretty much the WCW Belt (Physically) it does NOT share any of its history, it is a completely new belt created by the WWE, the actual WCW/NWA World Title History is in the WWE Championship, which was the Undisputed Championship, which was made up of the WCW Title, and the then WWF Title.
that is not entirely correct, either...when the NWA/WCW severed ties in the '90's, they both moved forward and the lineages split....WCW was the more visible obviously, but the NWA title went forward too, with guys like Dan Severn, Steve Corino, Shinya Hashimoto, Mike Rapada, and Sabu to name a few, holding the title until Severn ultimately was forced to vacate it, leading into the NWA_TNA era when Shamrock won it in the gauntlet match...so, niether of the WWE's titles has any sort of link to the NWA title