Who is legally entitled to a deceased parent’s property if there is only one child?

I am so sorry for your loss.  I am assuming that your parents dies intestate, meaning with out a Will.  Is that correct? And the property that remains was not jointly held with other parties or reciprocal beneficiaries?  Those assets may be considered joint assets and may pass to the joint account holder automatically.  It is necessary to see how they are held.  If the assets are not jointly held then the intestacy statute in the state of Hawaii applies.   Now it is unclear to me how the state of Hawaii distributes the share of your brother who pre-deceased your parents.  If they distribute per capita   then you would receive all the estate.  If, however, they distribute per stirpes then you would receive half of the proceeds and your brother's descendants would receive the other half.  You need to seek help from an attorney in the area familiar with the distribution process.  Good luck.

If there is no surviving spouse (which would include a separate, but not divorced, spouse), then the property all goes to the decedent's children. If there is one child, he would get it all IF there is no will (see below)...or more accurately, he will get all the property, if there is no will, that passes through the estate. Certainly property--real estate jointly owned with another; a joint bank account with another person; life insurance proceeds with a designated beneficiary; etc.--does not go through the estate. That property will go directly to the joint owner or designated beneficiary.

If there is a will, then the terms of the will control; the property will go to whomever is designated, and it does not have to be the child.