What is the ruling on keeping cartoon images on a mobile phone or computer, or using them as avatars on the internet? And what is the ruling if some body parts are uncovered in them?

The difference in fatwas regarding matters open to interpretation is not objectionable. The preponderant opinion concerning the ruling on keeping cartoon images and the like is that it is permissible in principle, as long as they are free from other Sharia-prohibited elements. The appearance of hair or arms and legs in them does not necessitate prohibition, as long as the image does not incite desires or cause temptation. Looking at drawn images differs from looking at real images.