In Illinois, you can avoid a probate if the decedent owned less than $100,000 in probate assets (that is, assets in his or her own name), and owned no Illinois real estate, at the time of death.
You can do so by presenting a small estate affidavit to the people or entities holding the decedent's assets: banks, insurance companies, IRA custodians, etc. The affidavit sets forth the facts -- that the decedent died (attaching a death certificate), that the decedent had or didn't have a Will (attaching a copy of the Will, if the decedent had one), etc. You also list the decedent's probate assets, and tell who should receive them in what percentages. The people or entities holding the decedent's assets should then distribute them as provided in the affidavit, thereby avoiding probate.
There's a small estate affidavit form in the Illinois Probate Act, but the form has a problem. Here's the relevant part:
7. (a) All of the decedent's funeral expenses have been paid, or (b) The amount of the decedent's unpaid funeral expenses and the name and post office address of each person entitled thereto are as follows:
Name and post office address Amount
(Strike either 7(a) or 7(b)).
8. There is no known unpaid claimant or contested claim against the decedent, except as stated in paragraph 7.