  In this paper, we extend the idea of comprehensive Gr\"{o}bner bases given by
Weispfenning (1992) to border bases for zero dimensional parametric polynomial
ideals. For this, we introduce a notion of comprehensive border bases and
border system, and prove their existence even in the cases where they do not
correspond to any term order. We further present algorithms to compute
comprehensive border bases and border system. Finally, we study the relation
between comprehensive Gr\"{o}bner bases and comprehensive border bases w.r.t. a
term order and give an algorithm to compute such comprehensive border bases
from comprehensive Gr\"{o}bner bases.
