The FAQ says that the ONE allows four segments per continent (except for the continent of origin). However, the itinerary planner only allows four sectors. And the fare rules state that it's four flights. I'm a bit confused by all this.

I would like to fly YYZ-TLS which has a transfer in LHR-LGW, for one sector (not including first intercontinental flight). I would then like to go TLS-DUB, which has no direct flight in the off season, for another two sectors. This means that I only have one sector left in Europe, which I would need to use to get to a major hub.

I don't plan to stopover (>24h) in any connecting cities.

So does this mean I only get to visit two cities in Europe on my ONE fare?

First, welcome to FT!

Second, four flights allowed in each visited continent except N. America (six.) Only two stopovers (>24h) allowed in continent of origin.

One flight number = one coupon. If you find a "direct" flight (e.g. LGA-RNO) that has an intermediate stop (e.g. DFW) but doesn't change flight number, then it's okay. Otherwise, one coupon per takeoff/landing cycle.

Thank you. I guess I may want to rethink my routing to YYZ-BCN via MIA and then take the bus/train to Toulouse.

I looked at the ONE rules and could not find any rule where I have to return to the country of origin (unlike the *A RTW). Does this mean it could be cheaper to get a one-way to Africa, and start a RTW there, but end it in North America?

No, it's right there in the rules -

72N . 4. TRAVEL MUST BEGIN AND END THE THE SAME POINT
73N . EXCEPT ORIGIN-DESTINATION SURFACE PERMITTED AS
74N . FOLLOWS:
75N . * WITHIN COUNTRY OF ORIGIN
76N . * BETWEEN U.S.A-CANADA
77N . * WITHIN AFRICA
78N . * WITHIN THE MIDDLE EAST
79N . * BETWEEN HKG-CHINA
80N . * BETWEEN BANGLADESH-BKK/SIN
81N . * WITHIN SOUTH AMERICA
82N . * BETWEEN MALAYSIA-SIN

Best you read the sticky threads at the top of this forum.

Happy planning!