With egg:
Use a mixer to beat egg whites and cream of tartar until foamy. Reduce mixer speed to low and gradually beat in the confectioners' sugar until blended, then beat on a higher speed until thick and glossy, about 2 minutes. (Add less confectioners' sugar if you don't want it to be too thick; use your judgment. Keep in mind that the thinner you make it, the runnier it will be when heaped on a cake.) Add warm water a tablespoon at a time if the mix is too thick.
Without egg:
Use a mixer on medium speed to combine meringue powder with water. Reduce to low and add confectioners' sugar gradually. Then beat at higher speed until thick and smooth, about 5 minutes. Add more warm water, a tablespoon at a time, if the mix is too thick.
Use either one as a nice thick icing for a cake!