No mortgage. I live there and provide P/T care, it was always my Mom and step-Dad's intent that my daughter and I would keep the house when they were gone. I'd anticipate issues with siblings & step-siblings but am more concerned with taxation issues.
This article may help distinguish the two, although I confess having read it several times and am still confused. (If the http: and www. prefixes are truncated by filters on the site, just add them back when you plug the URL into the address bar on your webpage.
thebalance.com/state-inheritance-tax-chart-3505460
This article and chart provide info on which states have inheritance or estate taxes:
taxfoundation.org/state-estate-tax-inheritance-tax-2018/
But you also need to consider step-up values, which occur on death. I don't recall all the issues so I won't offer any opinions other than that values can be "stepped up" to current value on date of death. I'm addressing that issue right now with mutual funds.
Some ancillary issues apply: do your parents have either a Will or Living Trust now? If so, was a deed prepared to "fund" the Trust with the house, and probably other assets? If not, in whose name is the house titled?
One's parents always want their child(ren) to inherit the house. With our parents living much longer [mine were in their mid-to-late 90's] they usually run out of funds for their care.
Once my Mom passed, then my Dad needed around the clock caregivers which cost him $20k per month. Dad decided to sell his house and move into senior living which was $5k per month so the equity from the house was a great relief.
So, getting the house would be nice, but realize that may not be the case. As for a Living Trust vs a Will, check with an "Elder Law Attorney" to see what is their recommendation.