The double-stranded molecule, DNA, has the unique property of replicat
ion and, because of this, it is the central molecule of life. The mech
anism of replication for each single strand is intricate, involving en
zymes which move along each of the single strands building a complemen
tary copy. At the frontier of this action, the events have a strong st
ochastic character due to the random location on the DNA of key 'sites
' where copying commences. A model of this process is analysed. The ce
ntral problem of interest is the mean length of certain 'islands' of n
ewly replicated DNA developed at the randomly located 'sites'. These i
slands, which have been observed experimentally, are called Okazaki fr
agments.