In British English, there is no difference between "farther" and "further". "Farther" is rarely used in British English (it sounds <em>very</em> awkward). The same applies to Australian and New Zealand English.

Officially, "farther" refers to physical distance and "further" to metaphorical distance in American English ("further" is also only used to mean "one more"). In practice, people in the US use them interchangeably. Keep in mind that while this 'rule' is taught by teachers in the US, it's never been part of the English language and was artificially introduced into the English language very recently. Long story short, an editor of the Oxford dictionary decided that this rule (invented by him) should be implemented into English. Others disagreed, and so the rule was taken out of the dictionary, but not before it entered the Merriam-Webster Dictionary (US English dictionary), where it remained for a long time (thus becoming a 'rule' of US English).

-http://www.oxforddictionaries.com/words/farther-or-further

-http://www.merriam-webster.com/dictionary/farther?show=0&t=1318599516

-http://www.quickanddirtytips.com/education/grammar/further-versus-farther

-http://random-idea-english.blogspot.com.au/2011/10/q-further-or-farther-british.html

Here's a simple answer - always use 'further' (comparative) and 'furthest' (superlative).

Farthest: This word exists, but it can only be used in certain contexts, to refer to physical distance only. For example, it is possible to say 'X is is farther away than Y', but not 'Do you have any 'farther' questions?'. If you mean 'additional', you can only use 'further'. There is never any <em>need</em> to use farther or farthest. As Jmat explained, the distinction is artificial and unnecessary.

Futherest:   ????   This is a nonsense word. It doesn't exist.

Furthest:  This is always correct, whereas 'farthest' is not always correct. You can use further/furthest any situation, literal or figurative.

"Centre" and "center" are respectively the British and American English spellings of the same word.

farther refers to distance or length. Further means additional or more.

Examples: He drove FARTHER than I.

               We need to research this FURTHER. 

Hope this helps.

Thanks for your answers, really helpful.