I have accumulated much material on all the Tichborne family and I am still working on it sporadically; there's lots out there!
I have been compiling a descent from Roger Tichborne (fl circa 1150) in Hampshire. It looks to me that all Tichbornes ARE descended from him. The Charles R C T, I mentioned is in a line descending from Robert T, the regicide though this is a little unclear in the early 18th C.
Robert is from the "Kent" Tichbornes who descend from a younger son (son=Morris? or Thomas) of John T and Margaret Martin (end of 15th C - and from whom descend also the main Hampshire lines (son=Nicholas) and the 'Chidiock' line (son=Henry).
The main Hampshire line is quite well documented. The 'Chidiock' line is difficult and I have not yet fully followed it. The 'kent' lines are complex and not well known but I have been pulling together information from various sources and have sorted out quite a bit of it. This line also seems to include many Tichbons including some in Australia. The regicide's line still exists in the male line with descendants in Kent and New Zealand. The Hampshire line died out in the male line with my grandfather, though my cousin still owns Tichborne Park.
There are Canadian Tichbornes who emigrated from Ireland and have spread to Australia and some now in London. I cant connect these up.
I am fairly sure that all Tichbornes before the Claimant disappearance of 1854 are one family. With the possible exception of some Touchburns from Ireland - they could be the originators of the Canadians - but also could be from a Kent line. After 1854 and the trials in the early 1870s some people assumed the name!
What's your interest in this? Email me if you would like a copy of my notes on the kent lines.