* Allies vow to pursue his efforts to unify hemisphere
* Chavez leaves legacy of economic problems at home
* Analysts: Will oil riches be given away as generously?
By Jeff Franks
HAVANA, March 6 (Reuters) - The death of Venezuelan President Hugo Chavez on Tuesday left a large void in the leftist leadership of Latin America and raised questions about whether the oil largesse he generously spread through the region would continue.
Allies such as Bolivian President Evo Morales vowed to carry on Chavez's dream of "Bolivarian" unity in the hemisphere, but in Cuba, heavily dependent on Venezuelan aid and oil, people fought back tears when they heard he had lost his battle with cancer.
His influence was felt throughout the region from small Caribbean islands to impoverished Nicaragua in Central America, and larger, emerging energy economies such as Ecuador and Bolivia and even South America's heavyweights Brazil and Argentina, where he found favor with left-leaning governments.
Without his ideological presence, Venezuela's influence is likely to wane and the pure financial weight of the Brazilian juggernaut could fill the gap in the region's diplomatic realignment.
Chavez, 58, leaves a mixed legacy of economic problems and political polarization at home, but for many Latin American and Caribbean countries he provided a financial lifeline and gave voice to regional aspirations of overcoming more than a century of U.S. influence.
"He used his oil money to build good relations with everyone," said Javier Corrales, a U.S. political scientist and Venezuela expert at Amherst College.
Venezuela's oil wealth also made it a major importer of goods from the region. "His import bill was so big, he became a major trading partner. That's why his relations were so good," said Corrales.
Between 2008 and the first quarter of 2012, Venezuela provided $2.4 billion in financial assistance to Nicaragua, according to Nicaragua's central bank - a huge sum for an economy worth only $7.3 billion in 2011.
Venezuela provides oil on highly preferential terms to 17 countries under his Petrocaribe initiative, and it joined in projects to produce and refine oil in nations such as Ecuador and Bolivia.
Chavez also helped bail Argentina out of economic crisis by buying billions of dollars of bonds as the country struggled to recover from a massive debt default.
"When the crisis of 2001 put at risk 150 years of political construction, he was one of the few who gave us a hand," Anibal Fernandez, a former cabinet chief in Argentina's government said on Twitter.
CREATOR OF BLOCS
Cuba gets two-thirds of its oil from Venezuela in exchange for the services of 44,000 Cuban professionals, most of them medical personnel.
That combined with generous investment from Venezuela helped Cuba emerge from the dark days of the "Special Period" that followed the 1991 collapse of the Soviet Union, the island's previous top ally, and has kept its debt-ridden economy afloat.
Chavez was close personally and politically to former Cuban leader Fidel Castro, with whom he plotted the promotion of leftist governments and Latin American solidarity against their shared ideological foe, the United States.
Along with Petrocaribe, Chavez pushed for the creation of the leftist bloc ALBA, or Bolivarian Alliance for the Peoples of Our America, and CELAC, or Community of Latin American and Caribbean States, both aimed at regional integration and reducing U.S. influence in the hemisphere.
"Chavez has been a regional leader with ALBA and CELAC, but ALBA has been in a process of gradual deterioration. In part as Chavez's health has deteriorated so has ALBA," said Frank Mora, former deputy assistant secretary of defense for Western Hemisphere Affairs in the first Obama administration.
"It's hard for me to believe that someone like (Ecuadorean president) Rafael Correa or (Cuban leader) Raul Castro can pick up the mantle that is being left by Chavez's absence (and) sustain the same level of support and vibrancy that these anti-American, Bolivarian relationships and organizations have had."
But, with his passing, the question now is what happens to both the oil riches he shared and the leadership he provided. Among other things, he played an important role in getting Colombia and the Marxist FARC rebels to hold their current peace talks.
Vice President Nicolas Maduro, his preferred successor, is favored in current polls to be elected as the next president in an upcoming election and is expected to continue his foreign aid programs.
But should his likely opponent, the more conservative Henrique Capriles, take the presidency, the largesse could end.
Capriles lost to Chavez in a national election in October, but made clear his opposition to his policies of giving away Venezuelan oil.
"To have a friend you don't need to buy him," he said during the campaign. "From ... 2013, not a single barrel of free oil will leave to other countries."
In 2010, Venezuela's state oil company PDVSA was not paid for 43 percent of its crude and refined oil products.
Chavez's high spending on allies has also taken a toll on the Venezuelan economy, which just underwent its fifth currency devaluation in a decade, experts say.
Chavez' leadership in Latin America, fueled by both his charisma and willingness to put Venezuela's oil money where his mouth was, will be difficult to replace, although other leftist leaders vowed to continue his programs.
"This process of liberation, not only of the Venezuelan people but also the Latin American people, must continue," said an emotional Morales in Bolivia.
"Chavez is more alive than ever and will continue being the inspiration for the people who fight for their liberation," he said.
The mustachioed Maduro, a former bus driver and union leader, shares Chavez's taste for anti-U.S. bombast, but not his flare.
"Chavez gave momentum, voice and leadership to the movement, but his leadership concealed the differences among all the leaders," said Christopher Sabatini, senior policy director at the Americas Society in New York.
"But the fiery, charismatic voice and symbol of that era - and that's what it was - has vanished," he said. (Additional reporting by Nelson Acosta and Marc Frank in Havana, Hilary Burke and Alejandro Lifschitz in Buenos Aires, David Adams in Miami; Ivan Castro in Managua; Jack Kimball in Bogotal; Eduardo Gil Garcia in Quito; Editing by Mary Milliken and Philip Barbara)