"They have people on their family tree who it would suggest are half aunts/uncles but names are blanked out as still alive. Likewise census records and stuff are only for older records so not sure what to do."
If you are on Ancestry then go back one generation (or more if necessary) to where there are names.
"...but names are blanked out as still alive"
Have a look at the parents of those people. Often, both (or sometimes just one) will have died and you can trace the names from there.
Here is an example:
So, let's say that the parents are called John Hardacre and Doris Arkwright (just made up names).
You find out that they married in, say, 1950. You then search the birth records. You leave the First Name box blank and put in Hardacre as the last name.
Put in a range covering ten years from the date of marriage. In this example, it's 1950 so that would be 1955 +/- 5 years.
For location, put in an area around where they were living.
Then, in the box for Mother's Last Name put in Arkwright. You can also use a wildcard here, eg Ark*, this will bring back all names that start "Ark... " if you are unsure of the spelling.
You then hit search and that will give you everybody with the surname Hardacre where the mother's maiden name was also Arkwright and they were born in that area in the timescale you are looking at.
This will likely get most of the relevant birth certificates (these would be the blanked out aunts/uncles).
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If only one of the grandparents has died (so the other one is still blanked out) then you would need to find out who the other person married before you did this.
Going back to the earlier example, if you knew that John Hardacre was the grandfather but the grandmother was blank you would need to find out who that John Hardacre married. You would find the marriage for him and Doris and then you could start the process above.
A couple of things to point out. If the family moved about quite a lot then you may not pick up all the children. Also, if they are common surnames then you may find another couple with the same combination of surnames (eg Hardacre and Arkwright) who were having children in the same area at the same time.
Finally, if the parents were unmarried then the birth certificate only gives the name of the mother and the child may be given either the mother's surname or the (alleged) father's surname. This can make it tricky tracing births as well.