  Very few examples of obstructed equsingular families of curves on surfaces
other than the projective plane are known. Combining results from Westenberger
and Hirano with an idea from math.AG/9802009 we give in the present paper
series of examples of families of irreducible curves with simple singularities
on surfaces in projective three-space which are not T--smooth, i.e. do not have
the expected dimension, and we compare this with conditions (showing the same
asymptotics) which ensure the existence of a T--smooth component.
