each hotel does their own thing. each case is different.

the problem with using a debit card is that the holds for authorization they take affect your daily balance and they take up to a couple weeks to get released. if you are in and out of hotels frequently, you could have a couple thousand tied up for a month in no time at all.

it is better to give them a credit card or give them cash (if you are not worried to be carrying larger sums of paper money). this way it is returned to you more promptly.