The ball is back in the Spanish king's court.

King Felipe VI started a second round of talks with Spain's political leaders Wednesday, renewing his tense search for a candidate to form a government following inconclusive elections last month.

The monarch was forced to resume his search after acting conservative Prime Minister Mariano Rajoy surprised many by turning down Felipe's nomination last Friday.

The lengthy period of haggling follows strong showings by a pair of upstart parties in the Dec. 20 election that upended the country's traditional two-party system.

The ruling center-right Popular Party won the most votes but fell short of a parliamentary majority.

Meanwhile, the new far-left Podemos and business-friendly Ciudadanos parties won substantial support from voters weary of high unemployment, a seemingly endless string of official corruption cases and disgust over the country's political status quo.

The result of the negotiations will determine whether Spain ends up with a government that could backtrack on unpopular austerity measures instituted in recent years or heads into a fresh round of elections.

As the period of high-stakes political brinkmanship enters a new phase in the eurozone's fourth-largest economy, here's a look at what is happening.

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A FRAGMENTED PARLIAMENT

The elections produced Spain's most divided parliament ever. Podemos and Ciudadanos smashed the dominance of Rajoy's Popular Party and the main opposition Socialists, which have alternated in government for decades.

No single party won a majority in the 350-seat Parliament. That is forcing the parties to consider brokering deals that would enable them to win the vote of confidence in Parliament that is required to take power following the king's nomination.

Rajoy's party won 123 seats, more than any other, while the Socialists bagged 90. The far-left newcomer Podemos and its allies won 69, while center-right newcomer Ciudadanos got 40 seats.

Amid the sniping and provocations between the parties, there is no sign of a breakthrough.

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THE KING'S REACH

With Rajoy out of the running — for the moment at least — the king is expected to turn to Socialist leader Pedro Sanchez when he meets him next Tuesday. But Sanchez, too, will have an uphill battle to muster parliamentary support.

When nominated, the candidate must win a majority in an initial vote of confidence in Parliament. Failing that, a second vote must be held with 48 hours in which the candidate would simply need most votes cast.

If no party leader manages to win Parliament support within two months of the first vote, fresh elections must be called. There is no deadline for either the king to select a candidate or for that person to hold the first vote.

The white smoke may take a while. "Clarity regarding government formation is unlikely to emerge this week," Wolfgango Piccoli, of the international consulting firm Teneo Intelligence, said in an analysis note Monday.

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RAJOY'S WOES

The Popular Party's ratings have plunged in recent years chiefly because of corruption scandals, unpopular laws and austerity measures brought in to help get Spain out of a severe economic crisis that started in 2008 and was marked by a double-dip recession and unemployment that shot up to 27 percent.

Rajoy had banked on the recovery — Spain is back among Europe's fastest growing economies — returning him to office. But his fall from a 186-seat majority in 2011, and the surge in popularity for Podemos and Ciudadanos, indicated most Spaniards wanted change.

Following the election, Rajoy offered to head a minority government with the support of the Socialists and Ciudadanos that would send out a message of stability to markets and Spaniards alike. The Socialists, however, said no.

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SANCHEZ'S CHANCES

Sanchez last week received an unexpected offer from the Podemos group to form a coalition government along with the small United Left party. That was seen as a smart challenge by Podemos leader Iglesias, and it has split the Socialists.

Some influential Socialists balk at the idea of joining forces with a radical, anti-austerity group it has been lambasting for several years. Sanchez, however, says voters from both leftist parties would not understand why the two can't see eye to eye.

The Popular Party and Ciudadanos, meanwhile, have already said they would reject that coalition in the parliamentary vote of confidence. The coalition would have 161 seats, leaving Sanchez still heavily dependent on six small parties that have 28 seats between them.

Spain has never had a coalition government.

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THE OBSTACLES

Major obstacles stand in the way of cross-party agreements.

For the Popular Party, the problem is other parties' complete rejection of Rajoy. Beyond that, Ciudadanos — the Popular Party's likeliest partner — would probably demand a reversal of public health and education cuts Rajoy said were vital.

Podemos would have similar demands to join the Socialists, but Podemos is also demanding that the powerful northeastern region of Catalonia be allowed hold a referendum on remaining part of Spain — a suggestion the Socialists, and the other two principal parties, vehemently oppose.

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THE MARKETS

One thing Rajoy can certainly boast is that his government was able to regain investor's confidence in Spain. When he took office in 2011, the country was teetering on the edge of a financial abyss and poised to request a bailout.

Some analysts, though, fear a prolonged spell with an acting government or a coalition involving Podemos may spook markets.