Transfer of Warranty of Deed upon death of co-owner

My Mother transferred her house from herself alone to both she and I by registering a new Warranty Deed in her county (in Nebraska).

At the time she executed the transfer, she explained to me that she was doing this so that the property would transfer to me upon her death rather than have to go through probate, particularly since she did not have a will. She was divorced at the time of the transfer and to her death. However, she had reconciled (but not remarried) my father and was living with him at the time of her death. Her reason for the transfer to me was so that she could ensure he could stay there as long as he wanted or needed to but still have the property go to her heirs (4 surviving children including myself) after he died.

It is now unclear whether or not the simple transfer from A to A and B (where A is my mother and B is myself) ensured what I think is called "joint tenancy with right of survivorship".

When I read the Nebraska statutes regarding this matter it is not clear to me how the state handles such things. There are numerous references to upholding the grantors intentions. I may have historical emails recording her intentions, but have no other documentation as such.

I am preparing my own will and would like to ensure this title is clean and clear.

Anyone familiar with the Nebraska Laws and willing to provide some guidance?

Thanks,

Tania