If someone assumes a loan on heir property, do then then legally own it?

I agree with everything stated above but also would like you to consider how the property passed -- was the deed written to reflect it passing to you and your siblings? Was the estate probated? Was there a will?

If probate was not open on the estate that brings up more issues and I would suggest also seeing a probate attorney in addition to a real estate attorney.

Unfortunately, paying a loan does not necessarily give one rights to property; often loans of various kinds (e.g. cars, homes) are paid by other parties, or have other parties on the loan, who are not owners. Ownership is separate from the responsibility to pay a loan.

That said, there are circumstances where it may be found by a court that a person's paying of a loan does give him or her some equitable right in or to the property, but that depends on the circumstances. It's also possible that it might be considered that in this case, a court could find there was an agreement between you and siblings to let you own the property in exchange for taking over the obligations.

You should discuss this matter with a real estate attorney, bringing with all relevant information and documentation. Remember: taking over the loan does not by itself convey ownership, but it might in some cases grant you ownership interest; and even if it does not, you may be able to at least assert a claim for reimbursement or contribution from your siblings. It's worth the consultation with the attorney.