It would appear that a reasonable arrangement has been reached on the Chair and Vice chair, and I'm pleased that councillors on all sides have taken a grown-up approach to those particular offices because like the speaker in parliament and non-executive mayors at district level, the holders have a responsibility to show a degree of impartiality when in the chair.
The Conservatives proposed an all-party inclusive administration (sometimes referred to as a rainbow coalition) and was also prepared to consider other options which would have given the county council a majority administration. Instead the Labour and Lib/Dem groups have announced that they will continue as a coalition administration, despite having only half the seats on the council(42 out of 84) between them. They presumably hope to limp along with support from some of the five independent members of the council. (This year they will also have the chair's casting vote, though they have promised the Conservatives the chair next year.)
This is not going to be a recipe for good governance: while this administration lasts I foresee full council meetings and some of the county-wide committees resembling trench warfare though I hope that constructive work can be done at some of the local and county-wide committees.