Short answers, pulled from the story.
Scientists at the Côte d'Azur Observatory in Nice, France published a triplet of papers in the general science journal Nature during 2005. This international collaboration proposed that four giant planets once occupied near-circular orbits with radii between 5.5 and 17 astronomical units.
The main motivation for introducing the Nice model was explaining a hypothetical surge in asteroid impacts on the lunar surface around 600 million years after formation. Icy planetesimals scattered onto planet-crossing orbits when the outer disc disrupted causing sharp spikes in impacts.
Recent measurements using laser ablation microprobe on the argon-40 to argon-39 isotope ratio on Vesta's surface contradict the bombardment timeline. Statistical artifacts combining finite uncertainty in age determination with the moon's cutoff age may create an apparent peak known as the Late Heavy Bombardment.
In this jumping-Jupiter scenario an ice giant scattered inward onto a Jupiter-crossing orbit then outward after encountering Jupiter. Step-wise separation avoided slow sweeping of secular resonances across the inner solar system.
A fraction of these planetesimals were captured via three-way interactions during encounters between two planets like Uranus and Neptune. The probability for a particular planetesimal to be captured by an ice giant reached several times one in ten thousand.