Rope Snake

From the Super Mario Wiki

Rope Snake is the name of Lucas's grab move, which also acts as a Tether Recovery in Super Smash Bros. Brawl. When Lucas uses a grab attack, he will use the Rope Snake to grab players from afar, and reel them close to Lucas for an attack. Lucas is also able to use the Rope Snake in mid-air, allowing him to grab onto an edge to get him back to the stage, in case he is too far to get back himself.

In Mother 3, the Rope Snake was a move used only by his partner, Duster, similar to how many of Ness's moves from the last two Super Smash Bros. games were used by his partners in EarthBound, not by Ness himself.