My condolences for your loss. The POA would lapse upon your mother's passing, so that should not be an issue. As to the joint accounts, if they included rights of survivorship then they would be yours and would not be part of the estate. Most joint accounts include rights of survivorship. Start by contacting the bank to find out how your accounts were actually held.
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I agree with Abraham's comments. In most cases, joint assets are held outside of probate however I don't have enough information to determine if your assets qualify. In any event, if the accounts are Payable On Death (POD), then they will pass outside of probate and be transferred directly to the beneficiary after providing the bank or institution with a death certificate, in most cases.
I agree with the previous two responses. Legally, ownership of a joint account passes to the joint owner, assuming the joint owner has rights of survivorship.
Sometimes an elderly parent will put one of his/her children's names on an account as a joint owner for the purpose of enabling the designated child to assist with banking and other financial matters. In this case, however, because your mother also designated your sister as POA, it would appear that she actually intended for you to be a joint owner on the account and for the account to pass to you at her death.
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I am very sorry for your loss. I agree with all previous responses. The only point I will add is that you should contact the bank as soon as possible. Although your mother's POA expired at the time of her death, your sister will remain on the account until the bank is notified. You should give a bank employee a certified copy of your mother's death certificate. Upon receipt of the death certificate, the bank will know that your sister no longer has authority to access the account.