FOR generations of American children and their parents, Legos were the ultimate do-it-yourself plaything. Little plastic bricks, with scant instructions, just add imagination.

In a wired world, they would now seem the ultimate anachronism, the only click being the sound of blocks snapping together. This holiday season, though, Lego is again among the hottest brands, and not just for the blocks, but a raft of Lego-related video games, children’s books and a TV spinoff — many of which are hugely popular in their categories.

In leading this revival of Lego, and creating a multimedia juggernaut, executives have shown great imagination. But some parents and researchers worry that the company’s gain has come at a cost to its tiny consumers: diminishing the demand for their imagination, the very element that made the Lego brand famous in the first place.

Even when actual bricks are involved, today’s construction sets are often tied to billion-dollar franchises like “Star Wars” and “Lord of the Rings” — and the story lines therein — and invite users to follow detailed directions, not construct their own creations from whole brick. It’s less open-ended, some parents and researchers say, and more like paint-by-numbers.