Are there [good/optimal] parallel comparison sorts? Comparing each pair of elements and sorting according to

[[number less than] minus [number greater than]] is a parallel comparison

sorting algorithm with a depth of $1$ comparison and $O\left(n^2\right)$ total comparisons.

By the AKS network, there is a parallel comparison sorting algorithm with

a depth of $O(\log(n))$ comparisons and $O(n\cdot \log(n))$ total comparisons.

1.
Are there any parallel comparsion sorts with a depth of

$o(\log(n))$ comparisons and $o\left(n^2\right)$ total comparisons?
2.
Are there any parallel comparison sorts with a depth

of $1$ comparison and $O(n\cdot \log(n))$ total comparisons?
(answering my own question)

1. $\:$ Yes

2. $\:$ No

Reference:

Tight Comparison Bounds On The Complexity Of Parallel Sorting

by Yossi Azar , Uzi Vishkin (1987)

publisher: Courant Institute of Mathematical Sciences, New York University

retrieved from http://archive.org/details/tightcomparisonb00azar (June 17, 2012)