If you've heard rumor that your ancestor was transported on a convict ship, you may be able to find some interesting details about them. Depending on where your ancestor was accused and tried, local Quarter Sessions records can describe origin, crime, punishment (usually transported for seven years servitude or for life,) to which colony, and by which ship. The Old Bailey, the London court where many criminals were tried, has an online index. The National Archives (UK) hold many documents relating to the transportation industry, including petition letters from family members wishing to join the exiled. There are many publications and online indexes of convict names sent to the Australian and American colonies, including the project I worked with, Immigrant Ancestors Project.
The ship records may include a doctor's description of your ancestor while on board. These descriptions could indicate the deportee's general health, physical description down to "blue eyes," "large nose," "pock-marked face," "scar on left elbow," and "other sundry marks." The doctor may have even described the intricate tattoos sported by many.
It is really interesting to note, however, that not all of these so-called criminals were tattoo-ridden rascals. Thomas Atwood of Surrey, for example, was sentenced to seven years transportation for stealing a sheep due to the "Cryes of his family for Bread, at a tyme, when he had it not to give them."
Another extremely interesting case is one Charles Peale. The son of a rector in England, he worked with the London Post Office. Somehow involved in a forgery there, Charles was sent to the American colonies around 1736. He purchased his freedom there, worked under the general postmaster for the colonies, and began a long career as a well-respected schoolmaster. He even attempted to gain the position of County Sheriff at one point. Charles wrote many letters to family and friends during his life, each one describing a man who desired to live a decent life, support his young family, and uphold his moral values. His oldest son, Charles Willson Peale, became famous in the cause of Revolution. He painted portraits of George Washington and Benjamin Franklin. He actively participated as a revolutionary supporter. He also made significant contributions in scientific studies.
For better or for worse, these deported citizens had an impact on the new lands they were sent to. The stories of these "convicts" are well-worth looking into. If you have an ancestor who was among them, you may be surprised at the facts you learn about who they actually were.