* Seven people from same family killed
* Attacks underline sectarian, ethnic tensions
* Thousands of Sunnis have protested against Shi'ite PM
BAGHDAD, Dec 31 (Reuters) - Explosions killed at least 10 people and wounded 46 across Iraq on Monday, police said, underlining sectarian and ethnic divisions that threaten to further destabilise the country a year after U.S. troops left.
Tensions between Shi'ite, Kurdish and Sunni factions in Iraq's power-sharing government have been on the rise this year. Militants continue to strike almost daily, and carry out at least one big attack a month.
The latest violence followed more than a week of protests against Shi'ite Prime Minister Nuri al-Maliki by thousands of people from the country's minority Sunni community.
No group claimed responsibility for any of Monday's attacks, which targeted government officials, police patrols and members of both the Sunni and Shi'ite sects.
Seven people from the same Sunni family were killed by a bomb planted near their home in the town of Mussayab, south of Baghdad.
In the Shi'ite majority city of Hilla, also in the south, a parked car bomb went off near the convoy of the governor of Babil province, missing him but killing two other people, police said.
"We heard the sound of a big explosion and the windows of our office shattered. We immediately lay on the ground," said 28-year-old Mohammed Ahmed, who works at a hospital near the site of the explosion.
"After a few minutes I stood up and went to the windows to see what happened. I saw flames and people lying on the ground."
Although violence is far lower than during the sectarian slaughter of 2006-2007, about 2,000 people have been killed in Iraq this year following the withdrawal last December of U.S. troops, who led an invasion in 2003 to overthrow Saddam Hussein.
Monday's violence also included a series of blasts that killed three people in Iraq's disputed territories, over which both the central government and the autonomous Kurdish region claim jurisdiction.
Two of those deaths were in the oil-producing, ethnically mixed city of Kirkuk, where a bomb exploded as a police team tried to defuse it.
Baghdad and Kurdistan are locked in a feud over land and oil rights and recently deployed their respective armies to the swathe of territory along their contested internal boundary, where they are currently facing off against each other.
Efforts to ease the standoff stalled when President Jalal Talabani, a Kurd seen as a steadying influence, suffered a stroke and was flown abroad for medical care earlier this month.
Maliki then detained the bodyguards of his Sunni finance minister, which sparked protests by thousands in the western province of Anbar, a Sunni stronghold on the border with Syria.
Protesters are demanding an end to what they see as the marginalisation of Iraq's Sunni minority, which dominated the country until the U.S.-led invasion. They want Maliki to abolish anti-terrorism laws they say are used to persecute them.
On Sunday, Deputy Prime Minister Saleh al-Mutlaq, himself a Sunni, was forced to flee the epicentre of the protests in Anbar's city of Ramadi when demonstrators pelted him with stones and bottles.