The report showed that iOS had made strides across most regions being tracked by Kantar, apart from Japan, Spain and urban China.
Android, meanwhile, continued to march on in all regions but the US.
"Gone are the days when a BlackBerry OS, Symbian, or Windows Mobile could make a significant impact," the report said.
The report showed that Windows mobiles were slowly disappearing from many markets. In Germany, marketshare fell from 5.9% for the three months ending January 2016 to 2.9% in the corresponding period a year later; in the US, the marketshare halved from 2.6% to 1.3% and in the UK the fall was even bigger, going from 8.6% to 1.9%.
In China, Windows mobiles went from an already minuscule 0.9% to 0.1%, in France they dropped from 7.8% to 2.8%, in Australia from 5.4% to 1%, in Italy from 7.2% to 4.4%, and in Spain from 0.8% to 0.4%.
In the five top EU markets of Great Britain, Germany, France, Italy, and Spain collectively, the drop was from 6.4% to 2.7%.
Only Japan bucked the trend for Windows mobiles, rising from 0.5% to 1.0%.
Kantar said in the US, overall Android marketshare for the three months ending in January 2017 was 56.4% of sales, a drop of 1.8% from the corresponding period a year ago.
iPhone sales rose to 42%, an increase of 2.9%.
In Asia, Android showed overwhelming dominance, accounting for 83.2% of the smartphones sold, a rise of 9.3%. Huawei (26.6%) was the top vendor, followed by Apple (16.6%) and Xiaomi (14.5%). The iPhone was the best-seller in urban China, but both Apple and Xiaomi continued to come under pressure from Oppo and Vivo.
"Xiaomi skipped the Mobile World Congress this year since they had no new devices to launch," said Tamsin Timpson, strategic insights director at Kantar Worldpanel ComTech Asia.
"Just as they did last year, Oppo made their presence felt at the show by debuting new hardware in the form of their 5x Dual Camera Zoom system rather than introducing a new device. Oppo, which sponsors Futbol Club Barcelona, have their sights set on growth beyond China."
Kantar said in the top five European markets, Android enjoyed 74.3% of sales. iOS held 22.7%, with the iPhone 7 being the top-selling device in the UK, France and Germany.
It anticipated that the two new Nokia Android smartphones — the Nokia 3 and 5 — could do well in western Europe as loyalty to the brand was historically high.
"HMD Global’s focus on revitalising the Nokia name seems concentrated on quality for cost. Its three new Android phones are priced at €229 or less, with Android Nougat, Google Assistant, aluminium construction, and otherwise solid mid-range specs," said Dominic Sunnebo, business unit director for Kantar Worldpanel ComTech Europe.
"While these models are not expected to rival the Apple iPhone 7 or the upcoming Samsung Galaxy S8, they do compete with other mid-range devices like the Huawei P8 and P9 Lite. Both of those Huawei models are strong sellers in price-conscious markets like Italy and Spain. This situation may present a new challenge for Huawei, as it pushes further into the premium end of the market with the debut of the P10."