* Market highly volatile on Brexit threat

* Safe-haven yen rallies, dollar drops below 100.00 yen

* Sterling hit hard across the board

By Ian Chua

SYDNEY, June 24 (Reuters) - Sterling suffered its most volatile session in living memory as the Remain and Leave camps took turns leading in Britain's referendum on its EU membership, triggering a rush into the safe-haven yen.

In the hours since the UK polling stations closed at 2100 GMT, the pound has swung in an eye-watering 15 cent-range, from around $1.3525 to $1.5022. At 0300 GMT, it was hovering at $1.3480.

"It is wild," said Shane Oliver, Head of Investment Strategy and Chief Economist at AMP Capital in Sydney.

Initially, there was optimism that Britain would vote to stay in the EU. Then early counts showed the leave vote gaining momentum, triggering panic across global financial markets.

On last count at 0230 GMT, the Leave camp was back with a slight lead.

Against the yen, sterling ricocheted between 135.30 and 160.14 and was last at 139.13, down a massive 11 percent on the day. The euro, which traded between 76.00 pence and 81.07, was at 80.12 pence.

"There is still a way to go yet," Oliver added. "Even if the vote is to leave, there is a lot of water to go under the bridge before Britain actually leaves the EU. We don't know what sort of deal they are going to cut with the EU."

As Brexit anxiety grew, so too has demand for the safe-haven yen, which jumped on the greenback and euro.

The greenback dropped below 100.00 yen for the first time since late 2013. The euro fell below 110.00 yen for the first time since late 2012.

The Australian dollar, often sold off in times of heightened market stress, fell heavily against the dollar and yen.

The Aussie shed more than three cents to $0.7306. On the yen, it was back below 75.00, having turned around from 81.61 yen.

Thin market liquidity played a part in exacerbating the moves, traders said.

"Many players are not trading actively," said Koichi Yoshikawa, executive director of finance at Standard Chartered Bank.

(Additional reporting by Hideyuki Sano in Tokyo and Rebecca Howard in Wellington, Editing by Eric Meijer)