By Steven Eke BBC regional analyst

Abkhazia fought for independence from Georgia in the early 1990s

His grip on power was much weaker than previously thought, and Georgians will be happy that his regime collapsed without bloodshed.

Georgia's President, Mikhail Saakashvili, says the "true revival" of his country can now begin.

Ajaria was his first real trial since becoming president, and he is clearly emboldened by the ease with which Mr Abashidze's rule was ended.

There is great pressure on him now to resolve the disputes with two other regions of Georgia - Abkhazia and South Ossetia.

Potential splits

Abkhazia represents the biggest potential danger.

Located in north-western Georgia, on the Black Sea coast, Abkhazia was famous for its citrus fruit and was home to holiday resorts in Soviet times.

Its people, the Abkhaz, are ethnically different from Georgians, and do not want to be part of Georgia. They have a historic affinity with Russia.

Abkhazia's war of independence in 1992-1994 - fought with Russian support - saw the entire Georgian population expelled.

Moscow still maintains a large military presence and has even issued the Abkhaz population with Russian passports.

The leadership in Abkhazia refuses to recognise Mr Saakashvili's authority, and has already warned him not to try repeating the 'Ajaria scenario'.

South Ossetia is less strategically important.

A small, landlocked region north of the Georgian capital, Tbilisi, it fought a war for reunion with North Ossetia (part of Russia) at the end of 1991.

Its leader, Eduard Kokoity, says he wants an admission of "genocide" from the Georgian leader before they can even meet.

A powerful neighbour

Russia views Georgia as being part of its 'natural sphere of influence'.

So Georgians will have been relieved by Moscow's apparent decision not to intervene during the Ajaria crisis.

Saakashvili and Putin want to strengthen ties

Many Georgians fear that their powerful northern neighbour might use unrest within Georgia to once again reassert its influence.

Despite previously having close links with Mr Abashidze, Moscow made no efforts to keep him in power.

That is a sure sign of how much Georgia's relations with Russia have improved since Mr Saakashvili came to power.

Future challenges

But if the Georgian leadership now wants to tackle Abkhazia, it might face a very different situation.

Many Georgians want the region re-taken by force, and some key officials have already said Ajaria was just the "first step".

In the event of a Georgian assault on Abkhazia, it seems very unlikely that Russia would remain passive.

Ajaria was about control of money, resources and personal power. It was a dispute between leaders.

That makes it very different from Abkhazia and South Ossetia, where the main issue is ethnicity.

Although clearly elated over Ajaria, Georgia's leadership also faces many other, formidable problems.