In a dry heavy saucepan (about 3-quart capacity) cook sugar over moderate heat, stirring with a fork until melted and then swirling pan, until sugar is a golden caramel, perhaps just a bit past golden towards amber, but not too dark.

Remove pan from heat and carefully add 3 cups water down side of pan (it will bubble up and steam). Return pan to heat and simmer, stirring, until caramel is dissolved.

Slice apricots and add to pan. Simmer until soft, about 10 minutes. Cool mixture 10 minutes and in a blender purée with vanilla until very smooth. Add any or all of the additional water if desired.

Sauce may be made several days ahead and chilled, covered. Reheat sauce to warm.