Hello,
It’s well to know that in the case of registrations of births, deaths, and marriages in the part of the United Kingdom designated together as England and Wales, which started on 1 July 1837, registration districts could overlap with more than one county. They were named for and listed as belonging to the place where the registration district was headquartered. In the case of Thorne r.d., this was Thorne in the West Riding of Yorkshire, a county adjacent to Lincolnshire on its northern border. (As a side note, ridings are something to google too as are the traditional divisions of Lincolnshire such as Lindsey and Holland)
If you google “Thorne registration district”, you will get some answers which explain this. A good place to visit is the first one appearing in my feed: www.ukbmd.org.uk/reg/districts/thorne.html
If you scroll through the listings, you will see that some places are in Lincolnshire (note the spelling as it’s mistyped in the question line and the tag) and others in Yorkshire.
You will find Amcotts at number two in the listings of the sub-districts of Thorne (YKS, for Yorkshire) registration district, and that it covered parts of Lincolnshire. The registration district existed from 1837-1947 when it was abolished and added to Don Valley registration district. The history of that r.d. is to be found on a a page you can visit from the Thorne r.d. page via the clickable link.
You will also learn there that even while Thorne r.d. existed til 1947, parts of Amcotts were transferred from Goole r.d. to Thorne r.d. in 1885, while Amcotts ceased existence as a sub-district of Thorne r.d. in 1938 when the sub-d. was transferred to Scunthorpe r.d. which was created in 1938 as headquartered in Lincolnshire. The subsequent developments in that r.d. can be followed on that clickable link in the notes for Amcotts sub-d. under Thorne r.d.
Counties generally have to be covered by several registrations districts. Not all registration districts started in 1837 exist today. They have changed with bureaucratic needs over the last 185+ years since their inception.
I hope this helps you get a handle on an important facet of jurisdictional knowledge that will help forward your research.
Regards,
Upton