OK, so for your stepfather to have been granted Letters of Administration means that he must have been married to your mum (an unmarried partner cannot do this).
I assume that this is in England or Wales (the rules are slightly different in Scotland).
Not everything that your mum owned will automatically come under the Intestacy rules.
Most homes are owned by a couple as "joint tenants". This is where you both jointly own the whole house (just like a joint bank account). So, when one of you passes away the house automatically goes to the surviving spouse.
If you own the house as joint tenants then the house automatically passes to the surviving spouse regardless of what any will or the intestacy rules might say.
Likewise, if any money or shares etc are in a joint bank account then that will automatically pass to the survivor without going through the Intestacy rules.
The other way to own a home is as "tenants in common". In this situation you each own a separate 50% of the home and you can leave your own 50% to whoever you like. In this situation it is usual for each spouse to leave their 50% to their children (but you can leave it to whoever you like).
A person's largest asset is usually their home so you will need to find out who owned the home and how it was owned.
You can do this by applying to the Land Registry for a copy of the title register of your mum's home here which costs £7:
https://www.gov.uk/search-property-information-land-registry
If it is just in your mum's name then she owns the whole house herself and it is part of her estate for the intestacy rules.
If it is in both their names then you need to check if the house is owned as joint tenants or tenants in common.
If you read the title and there is a restriction that reads something like this:
"No disposition by a sole proprietor of the registered estate (except a trust corporation) under which capital money arises is to be registered unless authorised by an order of the court."
Then that shows that they were tenants in common. What this means is that her 50% share of the house is part of her estate which will be distributed according to the Intestacy rules.
If there is no wording like that, then that means they were joint tenants.
If they were joint tenants then the whole house goes to your stepfather regardless of the intestacy rules.
In the same way, if she had bank accounts in her own name then they would be part of her estate but any joint accounts would automatically go to your stepfather.
.
So, assuming that the house was in your mum's name only or they were tenants in common and/or that she had bank accounts in her own name you then need to go on and look at the Intestacy rules.
The current rules say that the first £322,000 (plus all personal belongings etc) goes to the surviving spouse.
Anything above that amount is split 50/50 between the spouse and the children of the deceased.
Some examples.
1 Your mum owns the house and it is worth £300,000. She also has £20,000 in a bank account in her own name.
In this case, the total value of the estate is worth less than £322,000 so everything goes to your stepfather.
.
2 Your mum owns the house and it is worth £500,000. She also has £22,000 in a bank account in her own name.
In this case, her total estate is worth £522,000. Your stepfather gets the first £322,000 which leaves £200,000. This £200k is then split 50/50 between the spouse and the children. So £100k goes to the spouse and the remaining £100k is divided equally between any children.
So, in this situation your stepfather would get £422k and you would split £100k with any siblings you have who are children of your mum (so if she had children with your stepfather then they would also get a share of the £100k).