Exhibit 99.2

Holly Energy Partners, L.P.

Announces Results as of the Consent Payment Date on its

Previously Announced Tender Offer for 6.25% Senior Notes due 2015

DALLAS, TX, March 12, 2012 — Holly Energy Partners, L.P. (NYSE:HEP) (the “Partnership”) announced today that it and its wholly-owned subsidiary, Holly Energy Finance Corp. (together, with the Partnership, “Holly Energy”) have received the requisite consents in connection with its previously announced cash tender offer (the “Tender Offer”) for any and all of Holly Energy’s 6.25% Senior Notes due 2015 (the “Old Notes”) and the related consent solicitation (the “Consent Solicitation”).

As of midnight, New York City time, on March 9, 2012 (the “Consent Payment Deadline”), $157,761,000 million aggregate principal amount of the outstanding Old Notes (representing approximately 85.28% of the then-outstanding principal amount of the Old Notes) had been tendered. Holly Energy has exercised its option to accept for payment and settle the Tender Offer with respect to Old Notes that were validly tendered at or prior to the Consent Payment Deadline (the “Early Settlement”). Such Early Settlement is expected to occur today concurrently with the closing of Holly Energy’s previously announced offering of $300.0 million in aggregate principal amount of their 6.50% Senior Notes due 2020.

As part of the Tender Offer, Holly Energy solicited consents from the holders of the Old Notes for certain proposed amendments that would eliminate or modify covenants and events of default and other provisions contained in the indenture governing the Old Notes (the “Proposed Amendments”). Adoption of the Proposed Amendments required consents from holders of at least a majority in aggregate principal amount outstanding of the Old Notes. Holly Energy announced today that it has received the requisite consents in the Consent Solicitation to execute a supplemental indenture to effect the Proposed Amendments pursuant to its Offer to Purchase and Consent Solicitation Statement, dated February 27, 2012 (the “Offer to Purchase”).

As a result of receiving the requisite consents, Holly Energy entered into a supplemental indenture, dated as of March 12, 2012, to the indenture governing the Old Notes to effect the Proposed Amendments. The supplemental indenture became effective upon the Early Settlement of the Tender Offer.

The Tender Offer will expire at midnight, New York City time, on March 23, 2012, unless the Tender Offer is extended or earlier terminated (the “Expiration Date”). Under the terms of the Tender Offer, holders of Old Notes who validly tender their Old Notes after the Consent Payment Deadline but on or before the Expiration Date, and whose notes are accepted for purchase, will receive tender offer consideration of $983.00 per $1,000.00 in principal amount of Old Notes validly tendered plus accrued and unpaid interest from and including the most recent interest payment date, and up to, but excluding, the final settlement date, which is expected to occur on March 26, 2012. Other than in the limited circumstances set forth in the Offer to Purchase, tenders of Old Notes may not be withdrawn and consents may not be revoked following the Consent Payment Deadline.

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Holly Energy today also delivered notice that it had called for redemption all of the Old Notes that remain outstanding following consummation of the Tender Offer at a price equal to 101.042% of their face amount, plus accrued and unpaid interest to, but not including, the date of redemption. Redemption of the remaining Old Notes is expected to occur on April 12, 2012.

Requests for documents relating to the Tender Offer and Consent Solicitation may be directed to Global Bondholder Services Corp., the Information Agent, at (866)-540-1500 or (212) 430-3774 (banks and brokers). Citigroup Global Markets Inc. is acting as Dealer Manager and Solicitation Agent for the Tender Offer and Consent Solicitation. Questions regarding the Tender Offer and Consent Solicitation may be directed to Citigroup at (800) 558-3745 (toll free) or (212) 723-6106 (collect).

This press release does not constitute an offer to purchase, a solicitation of an offer to purchase, or a solicitation of consents with respect to the Old Notes nor is this announcement an offer or solicitation of an offer to sell any securities. Full details of the terms and conditions of the Tender Offer and Consent Solicitation are included in the Offer to Purchase. The Tender Offer and Consent Solicitation are made solely by means of the Offer to Purchase.

About Holly Energy Partners, L.P.:

Holly Energy Partners, L.P. (“HEP”) headquartered in Dallas, Texas, provides petroleum product and crude oil transportation, terminalling, storage and throughput services to the petroleum industry, including HollyFrontier Corporation subsidiaries. HEP owns and operates petroleum product and crude gathering pipelines, tankage and terminals in Texas, New Mexico, Arizona, Washington, Idaho, Oklahoma, Utah, Wyoming and Kansas. In addition, HEP owns a 25% interest in SLC Pipeline LLC, a 95-mile intrastate pipeline system serving refineries in the Salt Lake City, Utah area.

All statements, other than statements of historical fact, included in this press release are forward-looking statements, including, but not limited to, statements identified by the words “anticipate”, “project”, “expect”, “plan”, “goal”, “forecast”, “intend”, “could”, “believe”, “may” and similar expressions and statements regarding our business strategy, plans and objectives for future operations. These statements reflect our current views with respect to future events, based on what we believe are reasonable assumptions. Certain factors could cause actual results to differ materially from results anticipated in the forward-looking statements. These factors include, but are not limited to: risks and uncertainties with respect to the actual quantities of petroleum products and crude oil shipped on our pipelines and/or terminalled, stored or throughput in HEP’s terminals and tanks; the economic viability of HollyFrontier Corporation, Alon USA, Inc. and HEP’s other customers; the demand for refined petroleum products in markets HEP serves; HEP’s ability to successfully purchase and integrate additional operations in the future; HEP’s ability to complete previously announced or contemplated acquisitions; the availability and cost of additional debt and equity financing; the possibility of reductions in production or shutdowns at refineries utilizing HEP’s pipeline, terminal and tankage facilities; the effects of current and future government regulations and policies; HEP’s operational efficiency in carrying out routine operations and capital

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construction projects; the possibility of terrorist attacks and the consequences of any such attacks; our ability to consummate the tender offer; the impact of fees, expenses and charges related to the financing transactions described in this press release on HEP’s results of operations; general economic conditions; and other financial, operations and legal risks and uncertainties detailed from time to time in HEP’s Securities and Exchange Commission filings. Other factors described herein, or factors that are unknown or unpredictable, could also have a material adverse effect on future results. Please read “Risk Factors” in Item 1A of our Annual Report on Form 10-K for the year ended December 31, 2011. Except as required by securities laws, we do not intend to update these forward-looking statements and information.

FOR FURTHER INFORMATION, Contact:

Bruce R. Shaw, Senior Vice President and Chief Financial Officer

M. Neale Hickerson, Vice President, Investor Relations

Holly Energy Partners, L.P.

214/871.3555

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