  We study the existence of traces of Besov spaces on fractal $h$-sets $\Gamma$
with the special focus laid on necessary assumptions implying this existence,
or, in other words, present criteria for the non-existence of traces. In that
sense our paper can be regarded as an extension of [Br4] and a continuation of
the recent paper [Ca2]. Closely connected with the problem of existence of
traces is the notion of dichotomy in function spaces: We can prove that --
depending on the function space and the set $\Gamma$ -- there occurs an
alternative: either the trace on $\Gamma$ exists, or smooth functions compactly
supported outside $\Gamma$ are dense in the space. This notion was introduced
by Triebel in [Tr7] for the special case of $d$-sets.
