The boroughs of Liverpool, Knowsley, St Helens and Sefton were included in Merseyside. In Greater Manchester the successor boroughs were Bury, Bolton, Manchester, Oldham (part), Rochdale, Salford, Tameside (part), Trafford (part) and Wigan. Warrington and Widnes, south of the new Merseyside/Greater Manchester border were added to the new non-metropolitan county of Cheshire. The urban districts of Barnoldswick and Earby, Bowland Rural District and the parishes of Bracewell and Brogden and Salterforth from Skipton Rural District in the West Riding of Yorkshire became part of the new Lancashire. One parish, Simonswood, was transferred from the borough of Knowsley in Merseyside to the district of West Lancashire in 1994. In 1998 Blackpool and Blackburn with Darwen became independent unitary authorities. 

The Duchy of Lancaster is one of two royal duchies in England. It has landholdings throughout the region and elsewhere, operating as a property company, but also exercising the right of the Crown in the County Palatine of Lancaster. While the administrative boundaries changed in the 1970s, the county palatine boundaries remain the same as the historic boundaries. As a result, the High Sheriffs for Lancashire, Greater Manchester and Merseyside are appointed "within the Duchy and County Palatine of Lancaster".
What was the name of the two that started with "B"?
In Greater Manchester the successor boroughs were Bury, Bolton,