The Personal Representative of the estate for the deceased last owner (the last of your uncle and aunt to have died, assuming they owned it jointly with right of survivorship) would need to execute a deed over to you. I assume the PR would be your cousin. It's not very complicated, but will require an estate to be opened if one wasn't, or possibly re-opened if an estate was opened originally. Since you are the one who want's the property, I suggest you offer to hire the lawyer to get the paperwork done to accomplish this, and record the new deed in your name.

There are likely to be some expenses, but you can probably finance them by taking a mortgage on the property. First, title needs to be in your cousin's hands. Depending on the original names on the title, that may require opening the estate of the survivor of your aunt and uncle, or it may require opening both estates. There will be some expenses, inheritance taxes, and some legal fees, but they aren't that extreme for a transaction from parent to child. Your cousin will then need to convey title to you either as a sale from the estate or after taking title. There will be taxes on that transaction, as well. While the desire to avoid taxes is quite natural, the expenses of correcting the title increase dramatically if all the heirs from your aunt and uncle pass on before you fix this. Get a lawyer now, and work out how payment will occur. It is cheaper than losing the house.

An estate will need to be opened. If a married couple owned the property as "tenants by the entirety" when the first one died, title should have gone to the survivor of them. (If they owned title differently there may be a need for two estates).

In many cases an estate will require posting bond, publishing notice in the newspaper and filing inventories.

After record owners die, title can only be changed through opening up a probate estate, going through the estate process and then once the estate wraps up, deeding it out of the estate. Depending on how many other extended relatives are out there, it may make sense for the child of the owners (cousin) to disclaim their interest inside the estate OR it may make sense to inherit the property and gift it away after the estate closes. Inheritance tax usually applies when the person receiving property is a niece/nephew.

The above offers general information and doesn't take the place of getting legal advice about a specific situation. I strongly encourage you to seek legal advice for assistance navigating the estate process, preparing the necessary paperwork and for preparing deed(s) when the time comes. Even if you choose to administer an estate without legal counsel, getting legal advice to understand the process would help.