If a person dies without a Will and is survived by minor children, does the estate held in trust by the remaining parent?

Not necessarily, if the estate was acquired by you and the other person during marriage, then the deceased person share of the estate passes to the surviving parent. If this is a mixed marriage, and one partner brought the estate into the marriage with the children, then it appears the separate property estate of the deceased would pass to the minor heirs, to be held in trust by a surviving step parent or other designated guardian ad litem; seek the services if a probate attorney to assist you.

It sounds like the prior answer depends on the community property laws of states like California.  Ohio is not a community property state.

A very important consideration is -- was the deceased parent married at the time of death?  If so, under the Ohio statute of descent and distribution, the spouse inherits everything if the minor children are children of the deceased parent and the surviving spouse.  In this circumstance, the minor children would inherit nothing.

If the deceased parent was not married at the time of death, then the children will inherit everything.  Since they are minors, they cannot take title to the property.  It must be held for their benefit.  Ohio has enacted the Uniform Gifts to Minors Act and other provisions to make sure the property is held for the benefit of the minors.  The remaining parent may be the custodian of the property or, if this is not appropriate, someone can take action to appoint a professional or someone else to be custodian.

If the deceased parent was married but the children are not the children of the surviving spouse, then some portion of the estate will pass to the children.

This entire circumstance is complicated.  I agree with the prior answer that someone should consult a probate attorney to assist.