my friends live in laburnum and swear the deeds say their house was built in 1900, (I havent seen the deeds). However, on my os tranmere and oxton 1909, (1912 edition), laburnum doesnt even exist! (see attached scan of map). any ideas?

Does not seem to exist on the 1901 or 1911 Census, under address search, only.

Interesting that the start of the road is there at the Woodchurch Rd. end on the 1912 map.

Have a look at The Oxton Society, Oxton Road Names by Bob Knowles. Although Laburnum is not mentioned specificity it does say a lot of addresses went under just Oxton for many years.