Onesto is the second of five foals and the first runner out of the unraced Onshore (Sea The Stars), a half-sister to two winners, among them Jet Away (Cape Cross), winner of the Gr.3 Easter Cup and the Listed Festival Stakes in Australia and later a sire of jumpers.

Second dam Kalima (Kahyasi) also never raced and had six foals. She is a full sister to Arrive, dam of the Group 1 winner Promising Lead, and to the Listed winner Hasili, an outstanding broodmare whose Group 1 winners are Banks Hill, Champs Elysees, Intercontinental, Cacique and Heat Haze, while her son Dansili won at Group 2 level and became a sire. Kalima is also a half-sister to Skiable (Niniski), stakes-placed in the US, dam of the Group 2 winner and sire Three Valleys and second dam of Quadrilateral (Frankel), winner of the Gr.1 Fillies' Mile at two and placed in the Gr.1 1000 Guineas.

Third dam Kerali (High Line) was a winner and bred seven winners. Besides Hasili and Skiable they include Kid Gloves (In The Wings), dam of the Group 2 winner Treat Gently, and Kerawi (Warning), a stakes winner over hurdles. Kerali is also the second dam of two Group 1 winners who became sires, Leroidesanimaux and Uapybo.

Frankel has already succeeded with this family: Mirage Dancer, winner of the Gr.1 Metropolitan, is out of Hasili's daughter Heat Haze (Green Desert), who won the Grade 1 Matriarch Stakes, while Obligate, winner of the Gr.2 Prix de Sandringham, and the stayer Weekender both have Hasili as their second dam. Hasili is also the second dam of the Group 1 winner Romantica.

Onshore has a two-year-old filly by Australia and a yearling filly by Gleneagles.