I dont think he can draw down "too much" as a mortgage is for an agreed amount. He will draw down what was agreed to be drawn down i.e. the amount you asked to borrow from Ulster, lets call it X. The moment the switch is complete, you should owe exactly this X amount. How much was that? (it should be on every form you have). It must be more than E140K for sure as the solicitor will also take his fees from this, returning you the balance.
e.g.
Outstanding BOI E140,200
Requested borrow UB E143,000
Solicitor fees E1200
Solicitor clears BOI mortgage and takes his fees from your UB borrowing and balance is returned to you by solicitor 143,000 - 140,200 - 1200 = 1600
Owed to UB E143, 000 (it could be E143,100 as interest adds up quickly!)