Updates with details, background throughout

By Md Manzer Hussain and Hadeel Al Sayegh

June 4 (Reuters) - Shares of Saudi Arabia's Kingdom Holding Company 4280.SE tumbled as much as 10% on Thursday, erasing most of the gains recorded over the past week amid a surge of investor excitement over its stake in Elon Musk's soon-to-be-listed SpaceX SPCX.O.

Kingdom Holding's stake in the U.S. rocket company could be worth nearly $6 billion once it completes what would be the largest initial public offering on record.

Only a small fraction of Kingdom Holding's shares are free floating, which has contributed to their volatility this week.

Saudi billionaire Prince Alwaleed bin Talal holds a 78% majority stake in the company while Saudi Arabia's sovereign wealth fund, the Public Investment Fund, owns roughly 17%.

The shares had risen nearly 15% over the past week, but their precipitous drop on Thursday made the company the day's biggest loser on the Saudi benchmark.

Kingdom Holding said in a disclosure on Thursday that it owns a 0.34% stake in SpaceX valued at $4.47 billion at the end of March.

It added that, although the final IPO price and valuation are yet to be confirmed, should SpaceX's valuation reach Musk's target of $1.75 trillion, Kingdom Holding's stake would be worth about $5.67 billion.

SpaceX set a $135 per share price for its offering on Wednesday, targeting proceeds of $75 billion.

Market participants had already priced in a substantial financial gain resulting from Kingdom Holding's SpaceX investment. The Saudi firm's shares are up over 82% since the start of the year versus a less than 5% rise for the broader Saudi equity index.

Kingdom Holding has a decades-long track record of early-stage bets on global technology leaders. Past and present investments include Twitter before its takeover by Musk and rebranding as X, Careem before its acquisition by Uber UBER.N, ride-hailing firm Lyft LYFT.O and Musk's artificial intelligence startup xAI.

($1 = 3.7543 riyals)