Singalong, interesting one then for you happened yesterday.
Lead aircraft A340-300 filed FL340 requesting FL320 called on frequency abeam point A passing FL220 climbing at about 800ft/min with a groundspeed of around 380kts. Following aircraft B777-300ER was 11 miles behind and called on frequency about a minute later (as it also was abeam point A) passing FL250 (already 1500ft higher than lead aircraft) climbing with rate 2200ft/min filed FL370 requesting FL320 with a groundspeed of 425kts increasing all the time. The following aircraft was climbed to FL320 and the first aircraft given FL300. The B777 leveled about 25 miles after point A and the A340 about 45 miles after point A at which point they were only 3 miles in trail with the A340 in front. They stayed like that for over 100 miles and I would expect much further as they had filed the same route to the same oceanic entry point.
Hope that example shows that its not always first come first served in longitudinal senses, if you get to the level first then that can alter allocations.