  In the first part of the paper we give some bounds for domains where the
unitarizabile subquotients can show up in the parabolically induced
representations of classical p-adic groups. Roughly, it can show up only if the
central character of the inducing irreducible cuspidal representation is
dominated in an appropriate way by the square root of the modular character of
minimal parabolic subgroup. For representations supported by fixed parabolic
subgroup, a more precise bound is given. There are also bounds for specific
Bernstein components. A number of these upper bounds are best possible.
  The second part of the paper addresses a question how far is the trivial
representation from the rest of the unramified automorphic dual. By a result of
L. Clozel, trivial representation is isolated in the automorphic dual of a
split rank one semisimple group over a completion of a global field, but it is
very seldom isolated in the unitary dual (it can happen only in the archimedes
cases). Further, the level of isolation in the case of SL(2) is important for
the number theory. For the higher rank groups, the trivial representation is
always isolated in the unitary dual by an old result of D. Kazhdan. Still, we
may ask if the level of isolation is higher in the case of the automorphic
duals. We show that the answer is negative to this question for symplectic
p-adic groups.
