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The battle for customers between Amazon.com Inc. (NASDAQ: AMZN) and Walmart Inc. (NYSE: WMT) is well-known and well-documented. In one retail sector, though, the battle is between Amazon and Target Corp. (NYSE: TGT), and Target is not holding its own.

A new report from Coresight Research (formerly Fung Global Retail and Technology), took a look at consumer response to Amazon’s introduction of Amazon Fashion. The researchers in January surveyed 1,699 U.S. adults on how and where they shop for apparel.

Amazon and Target are essentially tied as the second-most-shopped apparel retailers in the United States. Amazon’s private-label apparel are the fourth-most-bought brand on Amazon’s website, and Target is the retailer losing the most shoppers to Amazon. The top-ranked retailer that respondents say they have shopped at is Walmart.

One of six takeaways from Coresight’s research is that two-thirds of Amazon Prime members surveyed have bought clothing or shoes from Amazon in the past 12 months, making Amazon the most-shopped retailer among Prime members. Among non-Prime consumers, Amazon tumbles to seventh place as a place to shop for apparel. Nearly half of shoppers expect to buy apparel from Amazon in the next 12 months.

Here’s a brief description of Coresight’s other takeaways:

One in nine Amazon apparel shoppers say that they have already purchased Amazon private-label apparel. The most popular apparel brands at Amazon are Nike, Under Armour and Hanes. Adult footwear and casual clothing are among the most bought categories.

The big battle in apparel retail is between Amazon and Target. Some 30% of Amazon shoppers spend more of their apparel budget than they once spent at Target. About 25% spend more than the once spent at Walmart and more than a fifth spend more than they once spent at either Kohl’s, Macy’s or J.C. Penney.

Younger shoppers are looking for an Amazon Fashion experience. These shoppers are most interested in trying Amazon Prime Wardrobe and the company’s private-label offerings.

Apparel shoppers like the Amazon Fashion website. Apparel is the fourth-most-shopped category on Amazon, trailing only books, beauty and personal care products, and electronics.

Nearly half of Amazon apparel shoppers continue to consider Amazon as an off-price retailer. Nearly half (48%) of Amazon apparel shoppers say they always expect to pay less than full price for apparel at Amazon.

The full report from Coresight Research offers more data and discussion.