  A random recursive cell splitting scheme of the $2$-dimensional unit sphere
is considered, which is the spherical analogue of the STIT tessellation process
from Euclidean stochastic geometry. First-order moments are computed for a
large array of combinatorial and metric parameters of the induced splitting
tessellations by means of martingale methods combined with tools from spherical
integral geometry. The findings are compared with those in the Euclidean case,
making thereby transparent the influence of the curvature of the underlying
space. Moreover, the capacity functional is computed and the point process that
arises from the intersection of a splitting tessellation with a fixed great
circle is characterized.
