* Conab slashes estimate of Brazil's total corn crop

* Technical trading, short covering gives soy, wheat a boost

* Lack of fresh demand news may cap rallies

CHICAGO, March 12 (Reuters) - Chicago Board of Trade wheat and soybean futures all turned higher on Tuesday as a stubbornly bear market gained support from weather issues in Brazil and a flurry of short covering as funds shift out of their huge net short positions.

Corn futures started the session out higher but turned lower by mid-day. Hot, dry weather is pressuring Brazil's moisture-loving Safrinah corn crop and boosting corn futures on questions of how that weather might impact yields, traders said.

Brazilian crop agency Conab slashed its estimate for the country's total corn crop to 112,753 million metric tons on Tuesday morning, down 943 million metric tons from February's forecast.

But a lack of fresh demand news was expected to cap gains on the day, traders said.

"There's no new demand," said Mark Schultz, chief market analyst at Northstar Commodity. "The trading is based on weather only."

The most-active wheat contract on the Chicago Board of Trade (CBOT) was up 2-1/2 cents to $5.49-3/4 a bushel, as of 11:16 a.m. CT (1616 GMT) on Tuesday. Wheat traded lower early in the session, but rebounded around mid-day.

CBOT Corn ticked lower at 1/2 cent to $4.41 a bushel, while soybeans added 6 cents at $11.85-1/4 a bushel.

Ukraine's diminished grain and oilseed harvest, as well as excessively rainy weather in France, may be playing a small role to boost wheat prices, analysts said.

The U.S. Department of Agriculture rated the same percentage of Kansas, Oklahoma and Texas wheat crop in good to excellent condition as last week.

Falling Russian wheat export prices and hefty global supplies continue to cast a bearish pall over wheat futures, and curb the competitiveness of U.S. wheat on the global market. Exporters cancelled sales of more than 504,000 metric tons of CBOT wheat destined for China within the past week.

"Wheat is the most bearish in terms of fundamentals, but it's still trading better," Schultz said. (Reporting by Heather Schlitz. Additional reporting by Naveen Thukral in Singapore and Sybille de La Hamaide in Paris; Editing by Sherry Jacob-Phillips, Mrigank Dhaniwala, Will Dunham and Emelia Sithole-Matarise)