Using the file that comes with a spell-checker in Linux (/usr/share/dict/american-english), I got "star" and "state". Upd: using another, larger one (483523 lines, /usr/share/dict/linux.words) I got "substantial". Hmmm...
As far as I remember from a very old article from a (then-)Soviet popular science magazine, the corresponding words in Russian are простор (prostor, spaciousness) and простота (prostota, simplicity). An interesting similarity: in both English and Russian the ties are -r vs -tV.
When I first read about this word game - I think I was about 10 y.o. at the time - I tried the same trick, albeit crudely, with a 50,000 word French-Russian dictionary, counting pages and columns rather than individual words for the first few letters, and got contrepoids (counterweight).
What is the "widest path" word in your language?