As these were getting built, did Laird sell them off or rented them out.
In 1843 Mortimer & Harwood street directory the highest number appears to be 38

Was lairds house number 63 the last house built or the 1st
Would the number of chimneys be for that many rooms in the building as the 3 sides (not including the Town Hall side) havw a middle house with 21 chimneys as against the rest having 13 or 14 and also 4 windows between the front doors while the rest only have 2 windows.

Numbering today from the station side then anti clockwise
1 to 18
19 to 34
35 to 50
55 to 57 then town hall then 58 to 63

The 1950s map shows number 51 as where Barclays Bank is (noticed it was closed up (possibly refurbishing it or closed for good)
No 51 now in Duncan St
No 57 is in Brandon st

I've noticed between 1843 and 1857 most of Hamilton Square had different occupants

http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&ved=0CD4QFjAC&url=http%3A%2F%2Fwww.wirral.gov.uk%2Fdownloads%2F2318&ei=iLb-UfOdEsm2hAegoIHgCw&usg=AFQjCNF8bF6DAqi8XB7IB697T8UgRIxSKA&bvm=bv.50165853,d.ZG4

Found this quite interesting, nothing on the chimneys though, used to work in 60/61/62 there was a rumour that Livingstone rented the front rooms of 62 whilst he was in Birkenhead.

wher did the stone come from to build hamilton square houses

Town Hall stone from Storeton Quarries though built later than the houses.Possibly Tranmere Quarry (in what is Old Chester Road now)
I think Laird used stone from Flaybrick Quarry when he started at Wallasey Pool

Storeton Quarry stone was used in the building of the Empire State building in America

Most of the stone from Flaybrick was used for Dock walls....

Ive heard that said before, but I could never find proof it was true any where. I know its off topic, but have you got any links?(besides Wikipedia)

I find it interesting that the Italian Consulate is just off there!

I think the story may be apocryphal. The Empire State Building was built in 1929, by which time the main quarries had been abandoned, and were soon to be filled with the waste from the Queensway tunnel. The South quarry, on the river side of Mount Rd. was still in intermittent operation, but the Storeton tramway had been dismantled so any movement of stone would have been by road.
The best clue I have is the book "The Storeton Tramway", by R,C,Jermy. In it, he says that Storeton Stone was used for: Birkenhead docks, Hamilton Square, Sankey Viaduct, the original Liverpool Philharmonic Hall, a house in Ireland and one in Essex. If it had been used in the Empire State Building I think Mr.Jermy would have known and mentioned it.