As the smartphone wars continue to heat up and some of the smaller vendors begin taking dead aim at Samsung and Apple around the world, the U.S. market, for right now, belongs to Apple's iconic iPhone.

An incredible 87 percent of Americans upgraded to a smartphone during the first quarter of 2014 and Apple's iPhone apparently led the way.

Apple's iPhone captured 36.9 percent of U.S. smartphone sales, while Samsung captured 33.1 percent during the quarter, according to a Counterpoint Technology Market Research report.

According to their research, the U.S. smartphone market reached 33 million units shipped at the end of the first quarter of 2014, with the smartphone market growing a modest 7% annually. Following the worldwide trend that is seeing smartphones overtake feature phones, the aforementioned figure of 87 percent of the total handsets shipped being smartphones opens up 2014 where 2013 left off. By the end of last year, worldwide smartphone shipments had officially accounted for the majority of all handsets shipped with an over 51% share, the fist time that had ever been the case.

Other points of note from the Counterpoint report included the fact Samsung remained the top overall handset supplier in the United States. Apple and Samsung together captured more than two-thirds of the U.S. smartphone market; Android share rose to 59 percent of the total smartphones shipped during the quarter; and Windows Phone share grew to slightly under 4 percent. Three out of four smartphones shipped during the quarter were LTE smartphones.

While the two leading smartphone makers are enjoying dominant numbers in the United States, the story is a bit different around the rest of the world. Several research firms that track the market have reported that despite rising first quarter shipment numbers for the overall smartphone category, market leaders Samsung and Apple actually lost share to their smaller competitors. Samsung share fell by 1.7 percentage points, to 30.2 percent, from 31.9 percent, and Apple's share slipped 1.6 percentage points, to 15.5 percent, from 17.1 percent, according to a recent IDC report.

According to Strategy Analytics, global smartphone shipments grew 33 percent annually from 213.9 million units in the first quarter of 2013 to 285.0 million in the first quarter of 2014. Smartphone growth was mixed on a regional basis during the quarter, with healthy demand in Asia counterbalanced by sluggish volumes across North America.