Abundant deposit inflows to Commonwealth Bank and to a lesser extent other major banks are a sign of a dash for safety by households and business, though maybe not to the detriment of smaller banks.Banking Day has heard talk that on one day last week CBA was deluged with around A$2 billion in inflows, and the numbers continue to draw smiles every day, though the bank disputed that this large number was correct.CBA highlighted the influence of its timely and (for a big bank) sharply-priced 12-month term deposit rate of 1.70 per cent, an increase of 0.60 per cent for both existing and new personal customers.The bank rushed this offer out the door minutes after last week's banking revival package and the blend of speed, intense public interest in the financial side of the COVID-19 crisis and the bank's franchise value have paid off."We have had a strong response to our offer, which means it has resonated with our customers," a bank spokesperson said.Judo Bank pay 2.15 per cent on the same term and have, on now dated figures, also done well on deposit inflows but the indications are the balance is - as in the GFC - favouring all big banks.The early signs suggest CBA's market leadership will once more be embellished by the epic economic collapse underway in Australia.Unlike the GFC, there seems (for now) to be no shunning of the smaller banks.Kevin Dupe, CEO of Regional Australia Bank yesterday said: "If anything, there is a move to us" on deposits.Asked earlier this week if there were any sign of a flight to safety at the expense of mutual ADIs, David Marshall, CEO of Defence Bank said there was no sign of that.In competitive spirit, Defence Bank yesterday lifted its 11-month TD offer to 2.10 per cent.In February, system-wide growth in household deposits was only 0.1 per cent and the lowest monthly expansions in the last five years. More than likely the preference for banks as savings vehicle reflects the dive in equity markets and expected returns on superannuation.