By C. Bryson Hull

COLOMBO, Oct 3 (Reuters) - Sri Lanka unleashed more air strikes on Friday on the seat of the separatist Tamil Tigers' quasi-government, and intensifying combat killed 42 in a relentless ground advance, the military said.

As battles raged across the front in the north of the Indian Ocean island nation, aid workers offloaded more than half of a 51-truck convoy, the first major shipment of food into the battle zone since the government barred aid groups last month.

Humanitarian groups say 200,000 people are trapped between the Liberation Tigers of Tamil Eelam (LTTE), who will not let them leave, and an army that has promised safe passage but which most victims fear and distrust after 25 years of war.

"The unloading of 29 lorries has been completed," the government's Commissioner of Essential Services, S.P. Diwaratne, told a news conference.

The convoy, carrying a week's worth of food, was being given safe passage by both sides, the United Nations said separately.

"We have no reports that should alarm us. It seems to be going according to plan, and the convoy is due back tomorrow," U.N. spokesman Gordon Weiss said.

The aid was delivered to four places between the LTTE-held northeastern port of Mullaitivu and their inland headquarters town of Kilinochchi, which is 330 km (205 miles) north of the capital Colombo, Diwaratne said.

That puts most of the refugees between the Tigers, and two prongs of the army's thrust. It is pressing north along the coast into Mullaitivu and northeasterly into Kilinochchi, a symbolic target that would give the already-confident military a morale boost. See [COL359082]

Air force jets hit the LTTE's police headquarters on Friday and a camp, both in Kilinochchi, air force spokesman Wing Commander Janaka Nanayakkara said. The rebels could not be reached for comment.

On Thursday, the day the aid convoy left, soldiers closed to within 3.5 km of Kilinochchi while the air force bombed the LTTE's headquarters, in a strike that prompted a rare confirmation from the guerrillas themselves.

Fighting throughout the day on Thursday killed 40 rebels and two soldiers, while wounding 52 guerrillas and 20 troops, the military said. There was no independent confirmation.

President Mahinda Rajapaksa's government is confident of finishing the conventional part of the war soon, having poured money and manpower at it since formally trashing a ceasefire in January that both sides had ignored for nearly two years.

The Tigers are the most ruthless and effective militant group formed to fight for a homeland for Sri Lanka's minority Tamil people. They have battled the government since 1983 in what is one of Asia's longest insurgencies.

In the process, the LTTE has eliminated all other militant Tamil groups, assassinated dozens of politicians including moderate Tamils, and been placed on U.S., EU and Indian terrorism lists for its widespread use of suicide bombings.

Sri Lankan Tamils have complained of marginalisation and broken promises from successive governments since independence from Britain in 1948, all of them led by members of the Sinhalese people who make up 75 percent of Sri Lanka's 21 million population. (Additional reporting by Ranga Sirilal; editing by Roger Crabb)

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