>

First off you’re not accounting for deaths, which low life expectancy is usually directly tied to infant mortality rates. Then you have 2 world wars where millions of people die, I’m not very well versed in the fine details surrounding the UK military at that time but America had zero problems grabbing Irish men fresh off the boat and putting them in boot camp, and I wouldn’t be terribly surprised if the UK did something similar.
If you want to get technical about it, those children born to children of immigrants aren’t Irish. They’re British. For both of those countries if you or your parents are born in that country then you’re eligible for citizenship. So if you’re grandparents moved from Ireland and you’re parents where born in Britain then there’s a possibility that you’re Identified as British at birth and the farther down you go the more likely that possibility is.
What am I missing here?

That historical records and community estimates are based on hand counted censuses whereas your analysis is based on a lot of mathematical assumptions that didn’t actually happen. >

Are you arguing that your estimates are better than census records? >

The British census data only includes Irish-born.
426,000 were irish-born in 1901, fifty years after the Famine.  The 2 million is an estimate.
But that doesn't include an unspecified number of second and third generations.
The historians and demographers come up with 2 million, but two cohorts born over a century (based on number of children born per women) would suggest 3x time as many offspring. >

You're assuming they stay in Britain instead of say, migrating to America or elsewhere >

You're missing death. People die. Children died especially often. Your model assumes that all children survive to adulthood, which is not the case. >

This is adjusted for death.  Surviving children per women.
I kick start deaths from the age of their 40s -and Im quite brutal insofar as Im basing only 60% reaching that, 70% for the generation after. >

What is your source for this adjusted number?