What are “Aborted Fetal Remains”?
Aborted fetal remains include all the body parts of a fetus who has been killed by abortion. In some cases, the fetus will be all in one piece. In other cases, especially second-term abortions, the fetus is dismembered for ease of delivery.
How are Aborted Fetal Remains disposed of currently?
State by State
There are no federal laws specifically concerning aborted fetal tissue disposal. This issue has historically been legislated by each state. Today, aborted fetal remains laws are a mix of state health codes, statutes, and regulations, according to a report released by the Charlotte Lozier Institute. 
Methods of Disposal
Former abortion clinic workers have described fetal body parts, including parts of larger babies aborted in the second trimester, being flushed down toilets. Those body parts end up in the city sewage system.  Fetal remains have been stored in freezers, and later incinerated.  They have been dumped in landfills.  One grotesque news story from Oregon reported aborted fetal remains being burned to provide energy for homes.  In another grisly news report, an abortion doctor carried around 15 jars of aborted babies in his trunk.
Michigan abortion clinic worker Renee Chelian , was a panelist at a 2015 National Abortion Federation Conference.  She spoke about storing fetal body parts in abortion clinic freezers for 5 months after her fetal remains and medical waste disposal company “fired us.”
She joked: “We were really tempted to give the fetus back. Um, we thought, we’ll give it to everybody in a gift bag – they can take it home, figure out what to do with it. It’s their pregnancy, and why is this our problem?”
Unborn Infants Dignity Act (UIDA)
The Unborn Infants Dignity Act (UIDA) is legislation drafted by Americans United for Life, and has been proposed in 28 states since 2016.  Americans United for Life is a pro-life public interest law firm founded in 1971. They “provide state lawmakers, state attorneys general, public policy groups, lobbyists, the media, and others involved in the cause for life with proven legal strategies and tools that will, step by step and state by state, lead to a more pro-life America.” 
The goal of UIDA laws is the humane disposal of human fetal remains.
Abortion rights supporters have claimed that this law would require burial of any fetus, regardless of gestational age or size. Others have stated that the law would require women who miscarry or abort at home to bring in their baby’s remains in a jar. In reality, UIDA legislation mandates that the bodily remains of aborted babies “who have reached a stage of development so that there are cartilaginous structures and/or fetal or skeletal parts and who are ‘expelled or extracted’ at an institution must be either cremated or buried.” 
Some states’ UIDA laws only apply to aborted babies. Others include stillborn or miscarried or both stillborn and miscarried babies. An example of Indiana’s UIDA law is here.
Why Should We Care?
In 2016, Indiana enacted a version of UIDA. Christopher Cooke, superintendent of cemeteries in Fort Wayne, stated in an article for The Atlantic: “Everyone deserves to go through the grief and loss process with dignity, from the individual we’re putting in the ground … to the family and friends who are paying their respects. This is a chance to give those individuals who don’t have anyone to fight for them the dignity and respect to go through a burial.” 
Some opponents of UIDA laws argue that because fetuses are not considered humans by the law while alive, they should not be after death. As detailed here, both federal and state laws recognize that a fetus is a human being. Examples of federal laws include the 2002 Born-Alive Infant Protection Act, 2003 Partial-Birth Abortion Act, and the 2004 Unborn Victims of Violence Act. Certainly, it’s contradictory to have laws that ban the murder of human beings, laws that acknowledge that fetuses are human beings, and laws that allow the killing of fetuses. However, the claim that current state and federal laws do not recognize the humanity of a preborn baby is false.
A complete listing of objections and AUL responses is here.
Recent Rulings on UIDA Legislation
In late March, 2019, the Ohio Senate passed UIDA legislation. It now moves on to the Ohio House of Representatives for a vote. This legislation was introduced once previously and passed in the Senate but not the House.
In Texas in September, 2018, a federal judge struck down a version of the UIDA with a permanent injunction. This means that the law will not be enforced. In his ruling, Judge David Ezra stated that the law imposed “significant burdens on women seeking an abortion.” 
It’s unclear what burdens he was referring to because women seeking abortions would not incur any additional financial cost due to the law. Instead, each abortion clinic would be financially responsible for any costs of cremation and burial or interment of ashes. In the Texas case, the plaintiff agreed that cost was not even a factor in whether the law should be upheld or not. Furthermore, the Texas Conference of Catholic Bishops offered to provide free fetal burial services to any hospital or abortion center in the state.
Though UIDA laws do not financially burden women seeking abortions, abortion supporters consider this type of law ‘burdensome’ because it: “increases the grief, stigma, shame, and distress of women experiencing an abortion.”  One wonders: if abortion is not the taking of a human life, what is there to be distressed about?
In response to Judge Ezra’s ruling, Joe Pojman of Texas Alliance for Life stated: “The unfortunate reality is that abortion will remain readily available in Texas and will occur tens of thousands of times every year. This law merely requires that the dignity of the unborn child is recognized after abortion and that their remains are not treated as medical waste.” 
Separately in Indiana, the 2016 UIDA law mentioned above was challenged by Planned Parenthood. Americans United for Life (AUL) filed a “friend of the court” brief requesting that the Supreme Court hear this case because it has implications nationally. The Indiana UIDA law’s constitutionality affects similar laws on the books or being proposed across the country.  
AUL’s brief noted that the humanity of the preborn human fetus has been acknowledged in such various areas of United States law as: tort law, guardianship law, healthcare law, property law, and family law.
Additionally, nearly all states have wrongful death statutes covering the death of a preborn human fetus or a fetus who is born but later dies from in utero injuries.
Finally, United States law has protections for survivors of failed abortions, also known as the 2002 Born-Alive Infant Protection Act, as well as a ban on intact D&X or dilation and extraction or partial-birth abortions.
What’s Really at Stake?
UIDA laws really get at the heart of the question:when does life begin? That is why abortion rights proponents are so offended by UIDA laws. If fetuses were not human beings, then their disposal would be the same as any other biohazardous waste from a doctor’s office or hospital, etc.
Since abortion clinics absorb the cost, not the pregnant woman, abortion proponents cannot object to the law for financial reasons (see Indiana case above). They object to the requirement that each pregnant patient and abortion clinic staff counselor have to address the humanity of the unborn child by deciding how to dispose of its dead body.
Tanya Marsh, a law professor at Wake Forest University, summed up the importance of UIDA laws this way for the 2016 The Atlantic article: “The most important impact of this law is taking another step toward recognizing fetuses as humans. That’s a philosophical goal of the law. It doesn’t have to do anything else except sit on the books and start to impact the way people think about it.”