Complete Vitamins
So how can a multivitamin say that it is 'complete' if it really isn't? Complete children's vitamins are 'complete' in the sense that they have some of all of the vitamins that your kids need. They just aren't 'complete' in having all of the recommended amounts of all of those nutrients.
And you wouldn't necessarily want a vitamin that has 100% of everything in one single pill, because as your child eats and gets some vitamins and minerals from his diet, then he will obviously get too much of many of those vitamins and minerals.
Incomplete 'Complete' Vitamins
Calling a vitamin 'complete' when it doesn't actually provide the 100% Daily Value for the vitamins and minerals in the multivitamin can be confusing and can lead parents to thinking that they are providing their children with adequate amounts of all nutrients, when they really aren't. This is especially true for calcium, which is often present in low amounts in most children's multivitamins.
Where It Stands
Remember that the AAP states that 'vitamin supplements should not be used except on the advice of your pediatrician,' so don't be quick to buy a multivitamin, which is likely incomplete anyway, without talking to your doctor.
In addition to guiding you to the right vitamin supplement if it is truly necessary, your Pediatrician might also be able to suggest dietary changes so that your kids can get any missing nutrients from the foods they eat, instead of a multivitamin.