No, actually none of it has. Antarctica is a desert so there is very little, if any precipitation. The ice comes from a unique weather system due to the continent's altitude relative to sea level. Most rain occurs far from the coast, but warm and cool air fronts can still collide on the continent which causes condensation (like dew) to form. Now there is moisture on the ground and the only step left in the process is the freezing.

1) "The south polar ice cap gets only 2 inches of precipitation each year (this is more than some deserts get). The accumulated ice never melts, is over 15,000 feet thick in some areas, and depresses the continental land mass under its weight (over 2,000 feet in some areas). The bottom of this ice pack may be over 100,000 years old and holds a record (layer by layer) of the history of earth with each layer." Source and further information: http://www.biosbcc.net/ocean/AAcontinent.htm 2 inches/year = 5.08 cm/year For 100,000 years: 508,000 cm = 5,080 m = 5.080 km 15 000 feet = 4.572 km 2) "The precipitation is carried in by the storm systems. These cyclonic systems carry warm moist air from the lower latitudes. So, most of the snow falls within 120 to 190 miles of the coast. Average precipitation on the coast is 20 to 50 inches of snow (7 to 16 inches of water equivalent). The Antarctic Peninsula has highest precipitation of the continent, (36 inches water equivalent). Precipitation declines inland because of the increased altitude and distance from the sea. Storms cannot penetrate far into the continental interior except in the low lying regions. Most snow fall occurs in winter when the westerlies are strongest and the storm systems can reach inland farther and more often. When warm moist air does make it all the way to the Polar Plateau, the air cools considerably. Eventually it becomes supersaturated with ice crystals. Ice crystals account for 90% of the accumulation on the plateau. The annual snow fall at the South Pole is less than 1 inch (water equivalent) or 3 centimeters." Source and further information: http://www.antarcticconnection.com/antarctic/weather/snow-ice.shtml "Diamond dust is a ground-level cloud composed of tiny ice crystals. This meteorological phenomenon is also referred to simply as ice crystals and is reported in the METAR code as IC. Diamond dust generally forms under otherwise clear or nearly clear skies, so it is sometimes referred to as clear-sky precipitation. It is most commonly observed in Antarctica and the Arctic, but it can occur anywhere with a temperature well below freezing. In Polar regions diamond dust may continue for several days without interruption." "While diamond dust can be seen in any area of the world that has cold winters, it is most frequent in the interior of Antarctica, where it is common year-round. Schwerdtfeger (1970) shows that diamond dust was observed on average 316 days a year at Plateau Station in Antarctica, and Radok and Lile (1977) estimate that over 70% of the precipitation that fell at Plateau Station in 1967 fell in the form of diamond dust (once melted, the total precipitation for the year was only 25 mm (0.98 in)." Source and further information: http://en.wikipedia.org/wiki/Ice_Crystals