There is some confusion over this topic because there is a difference between policies and procedures on European and American carriers.

With many European carriers (maybe it is a JAA regulation) it is common to have parents buckle in children on their laps with an additional belt that is totally separate from their own. In other words, the parent is buckled in with the main belt, and there is a separate belt attached to that, so that the parent does not smash the child into the single belt. There are two separate belts, each designed to absorb its own load, that of the parent and that of the child respectively. Think of a figure 8-- the parent is in the bottom loop of the 8; the child in the top. (Hope I described that well enough.)

(Note also that this is different from the traditional use of the term "seat belt extension" in the USA which refers to an extender to the original belt, still resulting in one belt once attached (but with two segments), which is generally offered to very obese people who cannot fit in the original belt. Think of a very big 0 made up of two seat belts clipped together.)

US carriers, on the other hand, have decided (or maybe it is an FAA regulation, not sure) that it is safer for parents to simply hold small children on the parents' lap with no belt.

On UAL, and I suspect on other US carriers, we simply don't have the child attachment belt available. Which believe me has led to some unpleasant encounters with parents who are used to the European method and think I am either lying or stupid (or both) when I try to explain this to them when they ask for the child attachment belt!