The election pits leaders of the wealthy northeastern region's separatist movement against candidates who want to stay part of Spain.
Record turnout is expected but with pro- and anti- independence candidates neck-and-neck in opinion polls, neither side is likely to win a clear majority.
The regional election is being closely watched across a European Union still reeling from Britain's shock decision to leave the bloc, and wary about any breakup of the eurozone's fourth-largest economy.
"I think many positions have become very extreme," said Assumpta Corell, a 21-year-old university student from the seaside city of Castelldefels who says she will vote for Ciudadanos, the centrist, anti-independence party that is scoring high in opinion polls.
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"People who have one opinion will maintain it, people who have a different opinion will continue thinking differently, which is great, but the problem comes when politics play at dividing people even more," she said.
"This is not a normal election," Puigdemont told supporters Tuesday evening in a final, virtual rally from Belgium.
"What is at stake is not who gets the most votes, but whether the country (Catalonia) or (Spanish Prime Minister Mariano) Rajoy wins" the standoff, he added.
While opinion polls suggest a narrow lead for Junqueras's leftist, pro-independence ERC, voters could ultimately hand victory to Ciudadanos, whose charismatic candidate Ines Arrimadas has campaigned on a fierce anti-nationalist ticket.
"We are very close to making our dream come true," Arrimadas told supporters at a rally Tuesday in a working- class district of Barcelona.
"We are going to wake up from this nightmare on Thursday," she added.
But ordinary Catalans on all sides of the divide appeared unsure the election would bring the independence crisis to an end, regardless of who wins.
"I'm anticipating problems, whoever wins," said Marc Botey, a 47-year-old musician, as he prepared to teach guitar to a student in Poblenou, a former industrial district of Barcelona that has since become hip.
"We want to know how many we are to be able to decide if it's worth it," he said.
With the separatist camp in disarray, secessionists will probably put their independence drive on hold even if they win the vote.
"Even if a pro-independence government is formed it will be very cautious how it acts because it won't want to lose the restored authority the Catalan government has," Andrew Dowling, contemporary historian in Hispanic studies at Cardiff University, told AFP.
The deposed government's independence declaration prompted more than 3,000 companies to move their headquarters out of the region, and no country has recognised the new "republic".
The Catalan crisis kicked off in earnest on October 1, when the regional government held a referendum on independence despite a ban by Spain's Constitutional Court.
The vote was marred by a brutal police crackdown and triggered Spain's worst political crisis in decades.
Neither separatist nor pro-unity parties are predicted to win a decisive majority in the 135-seat regional parliament, which could lead to lengthy negotiations to form a government.
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