Japanese, Hong Kong and Indian markets jumped in early trade on 23 January, as the European Central Bank's landmark quantitiative easing (QE) decision buoyed investors' risk appetite.
But the benchmark mainland Chinese and Korean markets pared gains towards the end of the trading session on Friday.
Hong Kong's Hang Seng was trading 1.13%, or 276.48 points, higher to 24,799.11.
India's Sensex was trading 0.84%, or 242.92 points, higher to 29,248.94.
The Japanese Nikkei finished 1.05%, or 182.73 points, higher at 17,511.75.
The Shanghai Composite finished 0.25%, or 8.42 points, higher at 3,351.76
Australia's S&P/ASX finished 1.51%, or 81.90 points, higher at 5,501.80.
South Korea's Kospi finished 0.79%, or 15.27 points, higher at 1,936.09.
In Tokyo, index heavyweight Softbank jumped 4%.
In Shanghai, insurers Ping An Insurance, China Life Insurance and China Pacific Insurance added 2%, 2.2% and 7.9% respectively.
In Hong Kong, Hutchison Whampoa was last up 2.54% after being halted from trading on news that the firm was close to buying UK mobile phone operator O2.
In Sydney, energy stocks rallied on higher crude oil prices. Santos shot up 5.1% while Oil Search and Woodside Petroleum gained 3.3% and 2.3%.
Miner BHP Billiton gained 1.9% despite weak iron ore prices.
In Seoul, automaker Kia Motors bucked the trend and lost some 2% after it reported a 54% drop in fourth-quarter net profit.
In Mumbai, JLR parent Tata Motors was trading 2.45% higher at 0723 GMT while rival automaker Mahindra and Mahindra was trading 3.15% higher.
Vodafone rival Bharti Airtel was trading 3.57% higher.
BofA Merrill Lynch said in a note to clients: "Oil was one of the biggest macro factors for Asia in H2 2014. In 2015, the bearish oil outlook will continue to weigh on Asia dynamics but a lot has already been priced in.
"Korea, India, Indonesia and Thailand are the biggest beneficiaries of lower oil price, while Malaysia will be the biggest loser."
Commenting on the ECB stimulus decision, Scott Schuberg, CEO at Australia's Rivkin, said in a note: "...I hope it works - Europe is a drag on the global economy, it is a drag on China and it creates concentration risk as the world looks to a continued recovery in the United States. We all want Europe to succeed.
"So what does this mean for equity investors? It's good. This was a big event on the radar, it was an event that had the potential to disappoint due to political discord in Europe, and it was something that no doubt weighed on the minds of investors who are willing to try and time the market.
"I would expect that cheaper access to funding out of Europe will create flows into higher growth and higher yield economies, and as those opportunistic players who can access money cheaply in Europe begin to implement their economic arbitrage strategies, emerging markets in Asia should benefit. As a result, Australia should benefit too."
Bill Adams, senior international economist for PNC Financial Services,commented: "...The ECB's programme includes "conditionality," or in plain English, "strings attached," to prevent eurozone governments from using it to delay austerity or economic reforms. The programme allows for purchases of sovereign bonds of all investment-grade issuers; countries like Greece and Cyprus, which are not investment grade and which are participating in economic reform programmes administered by the IMF, ECB, and European Commission, will have to comply with the terms of those programmes as a condition of having their sovereign bonds purchased by the ECB.
"The programme also includes some provisions to attempt to limit losses to other eurozone governments if another eurozone member defaults on its sovereign bonds held by a central bank. These loss sharing provisions are in our opinion unenforceable, but also unnecessary - the eurozone already had tools to force errant governments to cut spending and raise taxes if deficits became untenably large, and those are more important for enforcing fiscal discipline than the central bank loss sharing limits, which are the monetary equivalent of debating how many angels can dance on the head of a needle.
"To understand why loss sharing limits don't matter, consider that prior to the ECB's announcement, the German central bank was already lending €460bn to other European central banks to fund programmes analogous to the new asset purchase programme. In a riff on the old joke about bankers, if a central bank lends someone a billion dollars and the person can't pay it back, the person has a problem - if a central bank lends a person $460bn and the person can't pay it back, the central bank has a problem.
"In sum, the ECB's programme mildly exceeds expectations."