Abandoning/Surrendering Property

General Rule

The trustee may "abandon" property in chapter 7, 11, & 13 cases under 11 USC § 554.

11 U.S. Code § 554 - Abandonment of property of the estate
(a)  After notice and a hearing, the trustee may abandon any property of the estate that is burdensome to the estate or that is of 
inconsequential value and benefit to  the estate.
(b)  On request of a party in interest and after notice and a hearing, the court may order the trustee to abandon any property of the 
estate that is burdensome to the  estate or that is of inconsequential value and benefit to the estate.
(c)  Unless the court orders otherwise, any property scheduled under section 521(a)(1) of this title not otherwise administered at 
the time of the closing of a case is abandoned to the debtor and administered for purposes of section 350 of this title.
(d)  Unless the court orders otherwise, property of the estate that is not abandoned under this section and that is not administered in 
the case remains property of the estate.

In a Chapter 7, there is separate authority to abandon under 11 USC § 725

11 U.S. Code § 725 - Disposition of certain property
After the commencement of a case under this chapter, but before final distribution of property of the estate under section 726 of this 
title, the trustee, after notice and a hearing, shall dispose of any property in which an entity other than the estate has an interest,
such as a lien, and that has not been disposed of under another section of this title.

Notice and Hearing requires only an "opportunity for a hearing"

See 11 USC 102 and Bankruptcy Rule 6007 and its commentary.

Common practice is for the trustee to file a "Notice of Intent to Abandon" that is self-effectuating if no creditor requests a hearing.

In Chapter 13, sometimes referred to as "Surrender"

See 11 USC 1325(a)(5)(C).