  Aims: Based on our well-determined sample of open clusters in the all-sky
catalogue ASCC-2.5 we derive new linear sizes of some 600 clusters, and
investigate the effect of mass segregation of stars in open clusters. Methods:
Using statistical methods, we study the distribution of linear sizes as a
function of spatial position and cluster age. We also examine statistically the
distribution of stars of different masses within clusters as a function of the
cluster age. Results: No significant dependence of the cluster size on location
in the Galaxy is detected for younger clusters (< 200 Myr), whereas older
clusters inside the solar orbit turned out to be, on average, smaller than
outside. Also, small old clusters are preferentially found close to the
Galactic plane, whereas larger ones more frequently live farther away from the
plane and at larger Galactocentric distances. For clusters with (V - M_V) <
10.5, a clear dependence of the apparent radius on age has been detected: the
cluster radii decrease by a factor of about 2 from an age of 10 Myr to an age
of 1 Gyr. A detailed analysis shows that this observed effect can be explained
by mass segregation and does not necessarily reflect a real decrease of cluster
radii. We found evidence for the latter for the majority of clusters older than
30 Myr. Among the youngest clusters (between 5 and 30 Myr), there are some
clusters with a significant grade of mass segregation, whereas some others show
no segregation at all. At a cluster age between 50 and 100 Myrs, the
distribution of stars of different masses becomes more regular over cluster
area. In older clusters the evolution of the massive stars is the most
prominent effect we observe.
