By Sinéad Carew

(Reuters) - Shares of software firm Alfi Inc finished up 108.8% on Tuesday, one of the latest companies that has seen its stock surge in a broader rally that has refocused attention on so-called meme stocks in recent weeks.

Shares in Alfi closed at $16.29 after touching a high of $16.45, with 211 million shares changing hands, making it the third most actively traded stock on U.S. exchanges on the day. Its market cap has ballooned to $201 million, from a $15.5 million valuation for its early May stock market debut.

Some social media users and one portfolio manager cited a Benzinga.com report that Alfi planned to buy back stock as helping to fuel the rally. An investor relations representative for Alfi pointed Reuters to the report without providing details.

The stock had already surged almost 127% last week after it announced the rollout of tablets to Uber and Lyft drivers nationwide.

"They've had two great stories come out in recent days. It's a small company and doesn't take much to move the stock," said Daniel Morgan, portfolio manager at Synovus Trust in Atlanta, Georgia.

Volatility in stocks including AMC Entertainment Holdings and video game retailer GameStop have in recent weeks helped reinvigorate a meme stock craze that reached a peak in January, fueled in-part by retail investors congregating on platforms such as Reddit's WallStreetBets.

"I call this the casino corner of the stock market, all those highly speculative retail stocks that are being traded with no attention to what their actual worth is or fundamentals," said Ernesto Ramos, U.S. chief investment officer at BMO Global Asset Management in Chicago.

Other stocks that have recently captured investor attention include Torchlight Energy Resources, which was the second most actively traded stock on Tuesday, falling 29.4% after it increased its stock offering to $250 million from $100 million as it cashed in on retail investor interest in its shares. It had closed Monday's session up 58%.

Shares of GameStop, meanwhile, closed up just under 10% after announcing it raised about $1.13 billion in its latest share offering, cashing in further on interest in its shares.

Shares of AMC, which closed up 4.6% on Tuesday are up 2888% for the year-to-date, while GameStop's were still up about 1070% for the year so far even after paring gains dramatically.

Clover Health closed up 12.4% on Tuesday after rising as much as 25% earlier in the session.

(Reporting by Sinead Carew; Editing by Ira Iosebashvili and Lisa Shumaker)