For that big, old comet nucleus, with its much larger surface area would have experienced a huge amount of solar heating as it approached the Sun. It would've been a spectacular sight in the skies of our ancestors. Think of Hale-Bopp (on the left) but much bigger and brighter in the night sky. After interaction with Jupiter the new orbital period - a few years, rather than centuries or millenia - subjected this giant ice-world to more frequent and intense levels of activity. The rapid pace of the comet going around the Sun also accelerated its demise and fragmented the nucleus. Each fragment may have become a dramatic comet in its own right. As the centuries rolled by each fragment may have split further until complete disintegration occurred or until all the volatile materials boiled away into space - leaving, to all intents and purposes, an object resembling an asteroid.
And in the future? An intriguing object called Chiron, appears to be a giant comet although it was initially identified as an asteroid back in 1977. With a diameter of around 180 km Chiron has an orbit which takes it from within the orbit of Saturn to just beyond Uranus. Observations in the 1980s showed it to be developing a coma as it approached its nearest point to the Sun. Mathematical modelling also revealed the orbit of Chiron to be unstable and chaotic over long periods. In a million years it will probably have been put into a completely different orbit within the solar system or perhaps ejected completely the neighbourhood. But it can't be ruled out that Chiron will one day be a spectacular giant comet gliding regularly through the inner solar system.