ESTA visa and return fare

The requirement to have a round-trip ticket is imposed by statute, at 8 USC 1187(a)(8). It's not clear how this is enforced, or even whether it is regularly enforced. The requirement is not mentioned on the web pages of the Department of Homeland Security, Customs and Border Protection, or the Department of State:

• https://travel.state.gov/content/travel/en/us-visas/tourism-visit/visa-waiver-program.html
• https://www.cbp.gov/travel/international-visitors/visa-waiver-program
• https://www.dhs.gov/visa-waiver-program-requirements

Still, attempting to use the visa waiver program without meeting the round-trip ticket requirement seems risky indeed. The requirement is mentioned in TIMATIC, so an airline might indeed refuse boarding if you do not have the required ticket:

A return/onward ticket (or electronic ticket record) must be to a final destination country other than Canada, Mexico or contiguous (adjacent) countries or territories situated in or bordering the Caribbean Sea . If a passenger holds proof of residence in Canada, Mexico or a contiguous (adjacent) country or territory and is transiting the USA to that country or territory, then an onward/return ticket to that country or territory is accepted.

The definition of round-trip ticket, at 8 CFR 217.2(a), is somewhat loose, but that wouldn't help for someone who had no outbound ticket:

Round trip ticket means any return trip transportation ticket in the name of an arriving Visa Waiver Pilot Program applicant on a participating carrier valid for at least 1 year, electronic ticket record, airline employee passes indicating return passage, individual vouchers for return passage, group vouchers for return passage for charter flights, and military travel orders which include military dependents for return to duty stations outside the United States on U.S. military flights. A period of validity of 1 year need not be reflected on the ticket itself, provided that the carrier agrees that it will honor the return portion of the ticket at any time, as provided in Form I-775, Visa Waiver Pilot Program Agreement.

The ESTA is an authorization to travel to the US and apply for admission under the Visa Waiver Program.

According to the rules you can only use the VWP to enter if you have a "round-trip ticket" when you arrive.

The anecdotal evidence we have here is a bit equivocal about how strictly this requirement is enforced at the border in practice. But personally I wouldn't push my luck; it is plain that the border guards would be perfectly in their right to turn away a VWP traveler who arrives without a round-trip ticket, no matter how few or how many succeed in gaining entry without it.